Learn Polish: To jest mniejszy problem. - This is a smaller problem.

The base form is mały (small). This is an irregular comparative. Instead of just adding a standard ending to the word's stem, the word changes completely to mniejszy.

I've seen mniej used for "less". Why is it mniejszy in this sentence?

Mniej is an adverb (meaning "less"), which you use with verbs or to describe quantities (like "I sleep less"). Because you are describing a noun in this sentence (problem), you need the adjective form mniejszy (smaller). It behaves like a normal adjective and must match the masculine noun it describes.

Wait, doesn't the verb "jest" usually require the Instrumental case for nouns? Why isn't it "mniejszym problemem"?

Usually, yes! If you used a personal pronoun, it would take the Instrumental case (for example, On jest mniejszym problemem). However, sentences that introduce or identify something using the pointing word To (This/It) are a major exception. After To jest..., the noun phrase always stays in the Nominative (dictionary) case.

Can mniejszy be used for physical size as well as abstract things like problems?

Yes! Just like in English, you can use mniejszy for a physical object, like a smaller dog (mniejszy pies), or for an abstract concept, like a smaller problem (mniejszy problem).