I pay attention to the condition/cleanliness of the hallways and stairs in the building. If the owner can't be bothered to maintain any of that then you already know the apartment itself is going to be a mess as soon as something goes wrong.

A bit harder to judge but if it looks like other tenants/random people make a habit of hanging out in the hallways/stairwells then that's a massive red flag. One time I went to see an apartment and a guy inside the building on one of the stair landings was chilling out smoking a massive cigar next to the window.. I knew right away that building is always going to have cigar smoke.

This one might sound silly but I have a habit of testing the water in the bathroom and kitchen. That tells me what the water pressure is like as well has how well the hot water is working.

Maybe a bit nit picky but I usually bring a tape measure and do some quick room measurements to figure out if furniture is going to fit & whatnot.

Oh and like the other comment said it definitely helps if you know what the area and the building surroundings are like at night.