Teamfights is when things get nasty, given Ryze can only hit what's directly in front of him as Q doesn't pass units and that E->E->Q for spread damage takes a while to prepare and often fights would be over before you can do a single spread damage.
Also, mana management. Ryze has one of the worst mana/resource management in the entire game especially given his kit forces him to spam in spite of his pretty insane mana cost (combined with the low base damage all around), so for some his resource management especially for early game, takes a while to get used to.
Ryze is also very vulnerable if you have an hard engage champion as your opponent, and hard-engage comp on enemy side and enemy lane-camping would be your nightmares.
Then there is the ulti, it's quite hard to actually use especially the level 6 version. You need to have some good map awareness and foresight to use it properly in solo queue as a solo player, because no one would be watching your back or what's ahead of you and reporting it to you in efficient manner. With comms it reduces the strain of using Ryze's R which allows it to be an insanely strong if not OP spell under those settings, while in solo setting, it's very hard to use right most of the time, and is the biggest contributing factor to why there is such a rift between Ryze's professional and solo queue play. Honestly, Riot really should just change this ulti already, given it's nothing but a balance trainwreck.
Whatever the case, in solo queue, especially for those unfamiliar with Ryze, he's definitely not easy to play.