I believe that in Ptolemy's "Almagest" he just about managed to make everything work, but with a caveat, I think, that the earth still needed to be slightly off-centre. One of these days I might read that work, it's a triumph of ancient mathematics even if it is wrong.
But then there are degrees of wrongness, and sometimes this is under-appreciated. At the very least, the approach taken was fairly sound: gather data, as much as possible and as accurate as possible, and feed these data into a model to see if it works or not. Make adjustments to the model as necessary, and so on. In modern science, one would also attach an error estimate to the results obtained. That didn't happen until after the Scientific Revolution (and even then it didn't happen overnight); the result is that comparing Ancient scientific results to modern ones and saying "they were wrong then, they might be wrong now" overlooks the massive changes in the methods used.
There's also a risk that people read too much into things, of course. I think I'm right in saying that for early Greek Mathematicians the debate between Heliocentric and geocentric models was at the level of a purely theoretical model (which model fits the data better?) and then later people attached too much philosophical significance to the model, and became dogmatic about it to the point of viewing disagreement as "heresy".
This last remains a potential risk to scientists today, but so long as it's recognised that the Big Bang Theory is the most accurate description of the data to date, but that new discoveries may alter this position, the risk of too much dogma is minimal. It becomes much more a question of probability. It is at this point extremely unlikely that the BBT will turn out to be substantially wrong (although several details remain to be sorted out), and equally unlikely that competing theories will turn out to be correct instead. There is therefore no reason to expect this position will change in the future.