Problems with Shen:
1.(Damage Scaling) Shen's base damage scaling is just plain bad, i'm not sure whether to build AP or AD, which is the problem with many fusion champs. It seems like no matter what, the max damage Shen can ever do in his base Titanic>Flaming>Warmog (even with grasp of undying) is about 300-400 with Q, and about 170 or 180 damage base. His attack speed is so low that it doesn't even make up for the low damage dealt. I'm not sure whether i would be better off building gunblade and hexbelt with this champ or going pure AP or pure AD. The sad fact is his damage does not scale with his health that much if at all. A late-game Shen could be doing mid to early game damage at best against other champs that have maxed out crit and one shot capabilities.
2.(Ranged Vulnerability) Shen needs a ranged ability really badly OR a hook, and dodging a barrage of ranged attacks just to wait for the right moment to E, isn't ideal and leaves him super vulnerable. For an example, If you try to play as Shen top lane against Quinn, there is absolutely nothing you can do, hugging the tower just doesn't work for Shen and he is left absolutely defenseless. Even just farming the tower is impossible if you can't poke.
Solution: Make his Katana a grapple
3.("Tanking") For a tank that is supposed to charge into battle, his armor scaling isn't all that great. His attacks are under-powered and useless against a barrage of enemies, and he has ZERO crowd control making a double kill a nearly impossible feat.
4.(Lane Phase) Shen is not good at taking lane at all. It's difficult to get CS because of how slow his attacks are, and he absolutely requires Tiamat>Titanic Hydra. By the time Shen gets enough farm in top lane the enemy top lane already far out CS'es him. He is useless against just about every single top laner, they either have a ranged ability, have so much armor that it either ends in Shen doing 0 damage and dying (because Shen doesnt build crit or lethality), or a stalemate back and forth for 20 minutes in top lane... to be completely honest Flaming Cape only does so much.. It's getting to the point where Shen's only strength is Support, and he is no longer a top-lane tank.
5.(Support) Although Shen is slightly better at support, he still melts like butter against any champ with stuns, or silences, and his base Magic Resist is garbage. Early game against someone like a Lux, Morgana, Veigar, Lucian, Soraka, Miss Fortune, or even Jhin is pointless, unless your ADC is on point after your E taunt. He is clearly outmatched in almost every single lane.