Is the verb tense correct in this sentence?

Your sentence is in simple past, so you should keep verbs in base form.

You might solve some issues by coming here but might also face new problems.

However, if you want to include 'facing' in your sentence, then you should modify what precedes it by adding some phrases. For example, you can write it this way:

"You might solve some issues by coming here, though only at the cost of facing new problems."

This way 'facing new problems' collectively acts as a noun, or, to be precise, a gerund phrase.

Other ways of writing your sentence:

You might solve some issues by coming here, but you would also face new problems.

You may solve some issues by coming here, but you may also face new problems.

You may solve some issues by coming here, but you will also be facing new problems.