Corolla are very reliable. 11th generation (2014) looks different, has a longer wheel base and a more spacious interior but beside that and the CVT, underneath it's really the same as the 10h gen.
Some remains afraid of CVTs, because a lot of manufacturers screwed their first generations - and some are still on the road... - but it's the past.
Toyota have been using CVTs from Aisin for 16 years and the particular unit in Corolla for 3 years worldwide before bringing it to US 3 years ago without any particular trend/surge in complaints.
On forums, you'll sure find some odd cases, but no more than for the manual or 4AT (which is still available on the stripped L model).
They even have fake shift points to please the ears of those fearing the "drone" effect (maintaining rpm instead of constant up/down variation).
Basically, If you look on Consumer report or True Delta, there really is no dark point in terms of reliability. Of course, you never know how a particular used car has been maintained and driven !
Maybe check the headlights. The LED headlights are awesome and have a reputation to last "forever" but they cost an arm to replace