A lot. Much of it isn't really relevant to beginners, but here's a quick list off the top of my head. Maybe broken wasn't the right word, these are just general problems with the game
1. The endgame is too easy and boring.
2. Elbereth and #pray make it too easy to get out of tough spots
3. Most classes end up playing similarly after the midgame (either wizard or melee typically)
4. Wands of wishing, magic markers, and polypiling are too powerful
5. The game is nearly unbeatable without spoilers
6. Sokoban is boring after you've played through it a few times
7. There's a bunch of cheap tactics like pudding farming
8. It's too generic and boring to put together an ascension kit. There are very few trade-offs you need to make in choosing what armor and weapons to use
9. The religion aspect is too simplistic
10. Combat gets tedious in the endgame. Most of the time you're just plowing through monsters. This results in tons of "battle spam" with you getting several messages like "You hit the minotaur!" every turn, forcing you to not read them and possibly miss important information
11. The game requires several patches to be playable (menucolors, sortloot, hpmon, etc.)
12. The default options are pretty bad
13. Traveling and exploring can be boring
Wow, that was a lot longer than I thought it would be. But I only write so much because I care :) I had a lot of fun beating nethack and and it's one of my favorite games of all time. I'm possibly prouder of beating nethack than of my MS degree :)