I found that in the Egypt levels there are several Secrets that are activated by buttons. I was able to push the buttons multiple times, earning XP for each press. There did not appear to be a limit, I "found" over 200 secrets before getting bored.

Yes, it's there:
Egypt, 3rd level. There is a portal http://imagizer.imageshack.com/img921/3857/UkufWs.png
And nearby - a secret, and inside - another secret with a switch. Every time you press this switch - you will get "Secret Found" http://imagizer.imageshack.com/img922/1259/UH7Phk.png
With this "feature" - you can get eternal level-up
Just pressing this switch
And especially if you took perk "Scholar" - that adds random stat on every levelup :D
Also - to press a button rapidly - need nearly 30-40ms pause/latency between every pressing. 15ms - too short :D
even recorded video, getting megalevelups :D
https://youtu.be/yKz6scCYKUk