Most of the old photos I've handled/copied/etc are of a fairly thick card stock, perhaps 1/8th thick..maybe a bit less. The pictures are quite rigid, due to having been 'drying' for the last 60-100+ years. Often, they are oddly warped, as well. Typically, there may be water stains, bent corners, yellowed tape areas, photo-album stickum on the back, etc. One 'good' marker of a real old photo is broken-off/flaked-off image due to its brittleness...especially if the photo had been bent/creased. In my opinion, any photo paper newer than perhaps 50 years will not have image flaking off, exposing the white paper underneath. The paper qualities improved about WW II or thereabouts.
Often, multiple pictures from the same era will have different levels of fading, as well. Different people stored their pictures diifferently, resulting in different fade/yellowing/browning/discoloring.
Also, the focusing in the picture is typically soft compared to what we can get today, even with a kit lens. Fixed focus lenses of the 1800s and first half of the 1900s were merely a single piece of glass. Chromatic aberration correction and all the other fancy lens technologies hadn't been invented yet.
Genuinely old pictures sometimes have small white spots on/in them. This is easily spotted in the darker areas of the pictures. Just another 'look for' item.
Several years ago, I had the opportunity to 'fix' a handful of 1870s pictures for our local historical society. Two of the pictures had been creased right through the midsection of the bodies of the 15-20 workers in the pictures, standing for their portrait. I spent several hours on each 'cloning' the mens' clothing and surrounding stone quarry walls/rocks/etc. I also cleaned up various white dots and what nots, boosted the contrast a bit, and did a little sharpening in Photoshop, as well.
So, if the quality of the picture looks 'too good to be true', or if there's obvious cloning in the image, good chance it's a fake.