Is it OK to have a PhD thesis with shortcomings and inaccuracies?

The thesis is a "good" one if you have passed and will be awarded your degree. Don't overthink it. You have learned something from producing it that you can leverage into future work. That is, in lots of ways, a big advantage. If your advisor is also happy and wants to work with you on any future extension, you have a positive outcome, if not a perfect one.

That the thesis "might have been better, if only..." is true pretty frequently.

My suggestion is to take the advice of the reviewers and get done. Then write a future paper extending and improving on the thesis. Don't make it harder than it needs to be. Your dissertation shouldn't be thought of as your life's best work, only its first.

Don't let the perfect be the enemy of the good. (apologies to Voltaire)

Even if it is hard to consider when you are doing/have just completed your PhD, the thesis is not your magnum opus, but rather less-than-perfect showcase of your skills that was assessed as good enough by your peers to consider you as an autonomous researcher.

In a way, I would say that it is closer to a swimming certificate that proves that you can now swim by yourself in the deep end.

It doesn't mean that your technique is perfect, nor that you are an Olympic athlete. It only means you can now be considered as an autonomous junior swimmer that knows the basics, but of course will still benefit from guidance from experienced swimmers to get better and perfect its technique.

Almost all PhD students go through a phase right before their viva where they realise that the entire thesis is wrong and there is a significant, fundamental problem that brings everything down. That is rarely the case and it is quite possible you fall into that category. It is more common that the thesis has already known weaknesses in the form of incomplete parts that are not theoretically or empirically tightproof. To some degree, that happens in all theses. All of them have some sort of problem, shadow or error, although not to the point that the entire work is invalidated. There are also the cases of famous academics where they discovered years later that their work was all wrong or had been done decades ago by someone else but was forgotten in the meantime.

If there is indeed a problem and the examiners have not given you corrections on it, you have no reason to alter your thesis or spend an indefinite amount of time to improve it on your own. That would be dangerous. If you find that dishonest, you can add a paragraph explaining the potential issue that requires further research. You can then wrap up your thesis and turn this real or perceived issue into a new research question, which will give you a new paper.

(Not that this is the case with you, but I remember this time when I was reading a thesis from a world famous university only to realise that most of the equations were wrong. Fun times.)