imperfections before the presentation are like Edgar Allen Poe's "Telltale Heart"!!
I never try to clean up squeazings while theyre wet. With yellow glues it often times serves only to work it further into the wood. And in corners or other tight spaces that translates into a royal pain to try and clean up when dry. Or worse, to see no evidence only to have it go off like a metal halide spotlight when stain hits it!
The best Ive found is to work preventively in that department. Any glue that squeezes out (cannot be eliminated 100 percent) is extra glue that the joint didn't need (assuming you aren't the Hulk and over torqueing your clamps which sets a time bomb ticking for joint failure) Ive found using just enough to wet and have a little glue sitting on the surface, going back and lightly re wetting a long joint such as in a counter top glue up is sufficient. Making tops slightly over thicknessed allows for addressing any tear out. I will usually try to limit such glue ups to the end of the day when I wont need my bench then leaving them flat to dry overnight. Door panels don't always lend themselves to this practice due to the number of them glued at once but.... that goes back to limiting squeeze out. After the glue has dried I use a paint scraper followed by a sharp card scraper is all that is needed to clean up the joints then when final sanded any glue residue is gone and I rarely run into those "OH NO!" moments.
We all have imperfections in our work and as you mentioned that occasional loose tenon. Nothing wrong with putting epoxy or some other structural filler in there provided the joint isn't too loose a 32nd to a 16th is fine for epoxy. greater than that then you may want to either remake the part or plane and sand down a shim and glue that in place.
When I was out in the field trimming houses I always dreaded walking in on Monday morning and seeing My Friday afternoon work. And then Tuesday morning seeing what I did on Monday morning while angsting over my Friday afternoon work.... Funny the customers never noticed it but man I would look at it every time I walked by it.. And most times what we view as horrific is quite minor and never even noticed by the customer.
I think that demonstrates a level of care and pride of craftsmanship that we all share and separates us from those who just want to get it done and move on...
He who laughs last, thinks slowest