Formal:
* A plethora of problems: This emphasizes the large number of problems.
* A series of problems: This suggests a sequence or progression of problems.
* A multitude of problems: Similar to "plethora", this highlights the vastness of the problems.
Informal:
* A mess of problems: This conveys a sense of disarray and difficulty.
* A pile of problems: This implies a heavy burden of problems.
* A whole bunch of problems: This is a casual way to refer to a lot of problems.
More specific:
* A knot of problems: This is a good choice if the problems are intertwined and complex.
* A web of problems: This is similar to "knot" and implies interconnectedness.
Ultimately, the best collective noun for "problems" will depend on the specific situation and the desired tone.