Formal:
* A plethora of problems
* A myriad of problems
* A constellation of problems
* A cluster of problems
* A web of problems
Informal:
* A bunch of problems
* A heap of problems
* A mountain of problems
* A mess of problems
You can also use a noun that describes the specific type of problem, such as:
* A string of grievances
* A storm of complaints
* An epidemic of errors
Ultimately, the best collective noun for problems will depend on the specific situation and the tone you want to convey.