Here are two good ones:
The Jeffries signature looks bad to me for a number of reasons. First, it is faded but the supposedly contemporaneous inscription above and below it is not--you'd think the same ink exposed to the same conditions for 100+years would result in the same aging--and the date is partially written over the name [look at the J in July]. Looks to me like it was filled in later to make it appear that Jeffries had signed and inscribed it. Second, I don't buy the inscription date for Jeffries. The photo itself was taken July 4, 1910 and made into postcards, and this was supposed to have been signed three weeks later? Third, there is the image quality. The Dana photos from the era that I have seen are of much higher image quality, like this one:
Finally, it appears [you could tell better] that the other notations on the photo identifying various people match the purported signature. Seems more likely to me that it was made years later as a bar decoration and hand-annotated by someone to try and make it look like Jeffries had signed it.
And how does Dempsey come to sign it in 1931 in a bar in Alameda? Dempsey was active as a referee in 1931 so there is some record of his travels. The closest he got to Alameda for refereeing was Sacramento, which is several hours away in the pre-freeway days. And the signature is really messy for Dempsey--I've not seen a sloppy one like that, especially the first name.