I summarised the problems with Buddhist history in an essay entitled The Very Idea of Buddhist History.
There is only one reason to believe that Buddhist text are the words of the Buddha. It is because the Buddhist tradition says they are. There is no other reason.
Reasons for not believing are more numerous.
When we talk about the historical Buddha for example there is no corroborating evidence from another tradition that he existed. Buddhist texts mention the Jain leader, Mahāvīra, or at least we think they do. They never use the name Mahāvīra but do refer to a person called Nigaṇṭha Nātaputta whose views are very similar to the early Jains. See The Dictionary of Pali Names sv Nigantha. However Jain texts don't return the favour. Nor do the late Vedic texts record anyone called "Buddha". They do record many Gautamas, since the original Gotama was one of the ṛṣis who wrote the Ṛgveda, but not our Gautama. This is particularly surprising since Brahmins were frequently mentioned in Buddhist texts and they were actively composing new texts at the time. The first solid evidence for Buddhism is a brief mention in one of the inscriptions left by Asoka, ca. 250 BCE.
As far as the name Siddhartha Gautama is concerned, the Pāḷi version of the first name Siddhattha is never used of the Buddha in the Pāḷi Suttas. The name is a later invention. Indeed it had competition in the early Sanskrit Buddhist texts like the Mahāvāstu and Lalitavistara which tended to call him Sarvarthasiddha instead. What's more, as mentioned, Gautama is a high status Brahmin gotra (roughly "clan") name. Gotra names were used to mediate exogamous marriages. There is no obvious way that a non-Brahmin of that time, and of that culture which was not even part of the Vedic milieu, could have had a name like Gautama. If the name was adopted by the family, then it is strange that neither the Buddha's father nor any of his male relatives are ever called Gautama. It is even more strange that the Buddha's mother and maternal aunt were called Gautamī. Māyā wouldn't have changed her name at marriage. So it's possible that she as Prajāpatī were called Gautama and married into the Śākya family. Both Māyā and Prajāpatī are also distinctively Brahmanical names. The suttas have nothing to say on these matters. But the upshot is that we do not know with any certainty what the name of the historical Buddha was. I discuss this at length in an as yet unpublished article: Siddhārtha Gautama: What's in a Name?
What's more there are at least two biographical traditions about the early life of the Buddha. The standard narrative says that he is a prince, married with a child, his mother is dead, and leaves home in the middle of the night. And the alternative in the Ariyapariyesanā Sutta tells us he is a youth, does not mention any wife of child, and his parents are both still alive and present when he leaves. Since it is less familiar here is the Paḷi, with my translation.
So kho ahaṃ, bhikkhave, aparena samayena daharova samāno susukāḷakeso, bhadrena yobbanena samannāgato paṭhamena vayasā akāmakānaṃ mātāpitūnaṃ assumukhānaṃ rudantānaṃ kesamassuṃ ohāretvā kāsāyāni vatthāni acchādetvā agārasmā anagāriyaṃ pabbajiṃ. [M i.163]
At a later time, though still only a boy, with much black hair, in the first stage of life, and endowed with youth and good fortune; with my mother and father unwilling, tearful and wailing, I cut off my hair and beard, donned brown robes, and went forth from home, into homelessness.
The contraction cannot be easily revolved. I've discussed the contradiction and it's implications in an essay called: The Buddha's Biography.
A minor point is that the Pāḷi Canon is almost certainly a translation. No one spoke Pāli as a mother tongue, it was a lingua franca created for the purpose of recording the Buddhist texts. Of course it was probably very like the Prakrit or vernacular languages spoken in the region at the time. The Canon has quite clearly been edited and added to at different periods. Another problem is that by their own admission the texts were preserved orally for something like three centuries before being written down in Sri Lanka, ca. 100 BC. In other words the texts were preserved as stories told and retold. The dynamics of this kind of transmission are explored by Bhikkhu Anālayo in a paper called: Oral Dimensions of Pāli Discourses: Pericopes, other Mnemonic Techniques and the Oral Performance Context. It's clear when one reads the suttas that they are made up of modules - a bit like lego bricks. One meets the same bricks again and again in different contexts. This is typical of a story telling tradition. But it does not guarantee verbal fidelity. The best we could hope with three centuries of oral tradition, is that the suttas contain the gist of the what the Buddha, if he existed, might have said.
Another problem is that the Pāḷi Canon is inconsistent in some respects that make it unlikely to have been composed by one philosophical genius. For example dependent arising says
imasmiṃ sati idaṃ hoti... imassa nirodhā idaṃ nirujjhati.
when this exists, that exist... when this ceases, that ceases.
This means that when the condition ceases the effect must cease at the same time or immediately afterwards (this is implied by the grammatical form of the statement - a locative absolute using present participles). However for karma to work the effect (vipāka) must manifest long after the action (kamma)
has ceased. This problem was noticed by Nāgārjuna in the 2nd Century (Mūlamadhyamakakārikā 17.6). Another (topical) inconsistency is that between metaphysics and morality. The metaphysical insistence on the impossibility of personal continuity because there is no substantial entity to persist (anattā) contracts with the explicit personal continuity in the Jātakas and some suttas. These inconsistencies undermine the idea of the historical Buddha was we read about him in the texts.
Most of the innovations in Buddhist theory and practice have been because Buddhists have found the earlier accounts intellectually flawed and practically unworkable. The question of authenticity comes up constantly. Modern day Buddhists still compose apologetics for the authenticity of the suttas.
Over all what we see when we look with an open mind is a series of not entirely consistent stories about a traditional, legendary figure. His name is unknown, nor the language he spoke. Details of his biography are sketchy and contradictory. The literature which we take to be authoritative are characteristic of an oral, story telling body of traditional stories. The doctrines that we take to be the unifying factor of Buddhism on closer inspection turn out to be internally inconsistent (according to Nāgāruna anyway). We note that the Buddha was protagonist in our stories performed magic and miracles at times and that such stories are not distinguished from historical facts. And there is no external corroborations for any of the facts (which ever version of events we think are the authentic version).
If we are intellectually honest we have to admit that we know nothing at all about the Buddha for certain. There is doubt about every detail, about every word.
There are those who claim that we can trust the word of the Buddha because when put into practice the techniques work, for example Bhikkhu Yuttadhammo makes this claim in his answer to this question. In fact this is also rather doubtful. After 2500 years of practising what purport to be the very techniques employed by the Buddha, places like Sri Lanka, Burma and Thailand ought to be overflowing with arahants and every other person ought to be a stream entrant. But in fact there are at present no confirmed arahants in the world (I'm reliably informed that Daniel Ingram has recanted his claim). In which case the techniques in the suttas clearly do not work. Or at best they work rather partially to make people more relaxed about being unenlightened. If the suttas "worked" then many people would be arahants presently. So this argument from experience fails.
In the final analysis those people - both lay and scholars - who argue for the authenticity of the Buddhist texts either have to redefine "authenticity" to mean something less than 100% authentic; or admit that they are not willing to accept the facts and simply believe it to be so. In which case they are the same as religious people everywhere who just happen to believe that their teachings are the God's Honest Truth.
Which is not to say that the methods of Buddhism are not valuable. They are valuable. Extremely so. Just not in the way that the tradition or Traditionalists claim they are.