Back in college, for two semesters I had a roommate who had a bad stutter who was going through therapy for such. Really smart guy who went on to get a M.Ed. and become a teacher and coach. I remember at the time he'd have bouts where his stutter would get really bad, usually brought on by stress and/or fatigue; not only would he have trouble getting words out and, if he forced it, he'd end up sputtering out the wrong words instead of what he was actually trying to say or getting word order mixed up. Watching Biden in the debate last week reminded me of that -- someone who suffers with stuttering. Weird side-note, by the end of that second semester I had started to form a stutter myself, but fortunately it didn't last.
As far as cognitive impairment, keeping his stutter in mind, I don't really see it. Yes, he's slower and certainly has his gaffes, but overall he does seem cognitively present and aware. Of course I can only judge (like the rest of us, I suspect) by what I see in various news sources and on the boob tube. Mainly, though, when it comes to the election, I'm much more concerned with the administration as a whole rather than just the individual person running for POTUS.
I think what bothers me as well is just how much nitpicking there is going on as to what Biden said (or, yes, also didn't manage to say) but I see very little discussion over Trump's part in the debate. Typically during these types of debates, I'm accustomed to listening and picking out incorrect and false statements here and there, but in Trump's case, it was the exact opposite. I couldn't pick out any truths. I had a hard time picking out anything he said that wasn't, frankly, an outright lie. It was literally a flood of -- excuse my language -- bullshit that came out of his mouth. THAT is not normal and scares me way more than an elderly statesman who may have lost a step or two.