The number of arena levels is unlimited I believe. I'm up to 78 and the only difference seems to be the number of enemies you have to defeat to win. You reach a point where the difficulty no longer increases because the guys you face will be equipped with one of maybe 6 weapon loadouts. So long as you have a health gem in your weapon you can defeat them all without using any heal items.
Also, I've not noticed the game glitch in any harmful way. All that occurs is that you end up making too many fame achievements and coins to fit on the win screen, so the stuff at the top and bottom is hidden (drawn out of view). But you can just click like normal to go back to the menu.