The first thing I check is the edge, right where the print meets the frame. If it's a photograph or a print under glass, I want to see a mat or at least a clean border doing some work, not the image bleeding straight into the frame lip like someone rushed the layout. And I'll tip it toward the light to see what kind of glazing it has, because a cheap acrylic sheet throws a glare that makes half a room unviewable after two in the afternoon, and a cheap glass pane is an accident waiting to happen if it's anywhere near a doorway.
Paper fades, that's just physics, and a picture that hangs on a wall that gets afternoon sun for a few years will shift color whether you want it to or not, so I've started paying attention to where I hang things rather than hoping for the best. A sunroom gets the cheap stuff I don't mind replacing, a hallway with no direct light gets the one I actually care about. Frames age differently depending on what they're made of, real wood picks up small dings and a bit of a patina that honestly looks fine, painted MDF chips at the corners and then just looks tired, no in between. Dust with a dry cloth, keep anything framed in real wood away from a radiator or it'll warp slightly over time, and if the glass fogs or the colors look off behind it, that's usually moisture finding its way into a seal that wasn't done properly in the first place. In a room with a lot going on already, a plain room with a sofa, a rug, a lamp, one decent picture does more than three mediocre ones, and it sits better next to natural materials, a wood frame near a wood console, a textured mat near a linen cushion, than it does against a wall full of shiny metal and glass.
The real difference between a picture that looks good for years and one that looks sad by the second summer is almost always in the back, which nobody ever checks before buying, and they should. Flip it over. Is the backing board actual wood or dense board, or is it thin cardboard that will bow the second it's near any humidity. Are the corners of the frame mitered and glued tight, or is there a visible gap you could slide a fingernail into. Is the hanging hardware screwed into the frame itself or just stapled to the backing paper, because that second one will let go the first time a kid runs past and slams a door. None of this costs much more to get right, it's mostly about whether anyone bothered.
So before I buy one, I ask myself: if I turn this over right now, does the back look like someone built it to last, or just to ship?