One thing that in principle can be different is the crater patterning. However, it seems unlikely that has changed in any meaningful degree in human history.

Certainly not all craters have been dated, but a decent number has. You can access a crater Excel sheet on this page. I shortlist two that stand out:

• The crater named Giordano Bruno has an interesting history. In 1178 there is a well-documented event on the moon where "fire, hot coals and sparks" burst from the moon. It has been thought this was when an impact caused the creation of this crater. That would have been a change to the lunar surface that a keen observer would have noted. So at least Ceasar would have looked at a different moon than today. However, this theory has been doubted since there is no record of an associated meteor storm on Earth, as would have been expected. So this is at least a young crater, but probably not as young as 1178.
• The crater named Eimmart A is noted in the database as "very young". It is a small crater, however (~7 km diameter), and when the lunar people say "very young", they mean it is "probably less than 100 million years ago". So sure, maybe it might have formed early during the human era. Still, not that likely.

From what I can tell, a major crater formation that would change the appearance of the moon viewed with eyes would generate a great deal of meteors on Earth, like when comet debris hit Earth. I do not know enough obscure history, but if a major crater formed while there were literate humans on Earth, then maybe they would have recorded that as some great mystical event.

So in short, my best guess is that major crater formation that would alter the view of the moon during human civilization is unlikely, but possible.

My guess is that light pollution from cities are a bigger difference in how the moon appears to us and to Ceasar.