Add some additional checks to the acceptance mempool test

[oxarbitrage]

Motivation

We want to check some additional stuff to the mempool acceptance test we added at #2862

Close #2691

Solution

Add missing checks.

Review

The code added here is short, so anyone can review.

Reviewer Checklist

• Code implements Specs and Designs
• Tests for Expected Behaviour
• Tests for Errors

[teor2345]

This is a good idea for a test.

But I'd like to create a new test, rather than re-using the existing one.
A new test could sync more blocks, and get better test coverage.

I also made some suggestions for making the test more reliable.

[teor2345]

I just committed a minor fix, we should be good to merge now

[teor2345]

I'm auto-merging this PR, so upcoming PRs are better tested.

Thanks!