As always after a presidential debate, I would like to remind people that the impact of these debates on a campaign isn't decided by pundits or by people who follow politics closely (like me and most of those reading this post!). It's decided by swing-voters, most of whom are ignorant about politics and government, inattentive, and far less likely to watch the debate than people with strong partisan commitments. Thus, the impact probably won't be as big a catastrophe for Biden as pundits now say. We will know more when we see post-debate polls.
That said, Biden acting like a doddering old man is the kind of problem even relatively ignorant voters can easily understand. My 9 year old daughter noticed it while watching the debate (Biden seemed "overwhelmed," she said), and swing voters who saw it likely noticed as well. And it's a problem MORE easily noticeable by the ignorant than Trump's many lies and distortions (which require some preexisting knowledge to see through).
The best Biden can hope for is that the news cycle will shift, and people won't remember this debate 2-3 weeks from now. It's also possible he had an unusually bad day. But if this is how he really is now, he might repeat the performance in the second debate and have other unfortunate senior moments. If so, it may still only cost him a couple points (a huge proportion of the electorate has made up its mind and won't shift its partisan loyalties). But a couple points can be decisive in a close election.
Aside from electoral considerations, there is an inherent risk to nominating an 81 year old man, who will be 86 by the time a second term ends. Cognitive decline is VERY common at that age, and could easily get worse quickly. I have seen it happen.
For both electoral and substantive reasons, it would be good for the Democrats to replace Biden with a younger, fitter candidate. Many have said that tonight. But, obviously, it will be almost impossible to do unless he bows out voluntarily. If he IS willing to bow out, I wonder if he might be best served by not only dropping out of the race, but resigning the presidency (pleading a sudden downturn in his health). That would make Kamala Harris the incumbent, and give her a small boost in the polls. Yes, it would be only a couple points or so. But that could be important. Ideally, of course, the Ds nominate someone more popular and competent than either Biden or Harris. But getting them both to step aside seems virtually impossible.
Don't get me wrong, I still think Biden is less bad than Trump. Mildly senile with a lot of cruddy policies (as well as a few good ones) is less bad than a deeply evil man with a deeply evil agenda. And Trump's own cognitive capacities are far from great. But it doesn't really matter who I would vote for. What matters is the swing voters I mentioned above! Polls consistently show they are concerned about Biden's age (so am I; I just hate Trump more), and those concerns could well get worse now. If that costs Biden even a couple points of support, he very likely loses the election. And even if he still somehow wins, cognitive decline will be a hazard in his second term.