Do researchers make more mistakes as they continue to work in a discipline?
I think it's not that you're making more mistakes (not that I know 100%, to be honest) but that you are becoming more aware of the subtleties of your field, and are therefore becoming more aware of the difference between, say, a well-studied, published researcher and yourself.  As you learn what is and isn't important, you start to recognize that you need to be more precise and rigorous.

The best advice I have for you is to take note any time you make such a mistake.  Why was it made?  Was it because you just wanted to write something down andget through it?  Was it a genuine misunderstanding?  Was it because you understood exactly what you meant, so you assumed that others did too?  etc.  Then, address the individual causes.

One of my biggest issues was the latter - I knew what I meant to say, so I didn't bother to be careful defining my terms or the context.  It was obvious to me, so I forgot that I had spent months figuring it out and therefore it wasn't obvious to anyone else.  I took a long time to remind myself that a proper setup  is extremely important in selling the relevance and impact of my work.  I still make that mistake sometimes, but I'm at least more aware of it.