Firstly I added the bugs that I've seen by myself, as I've seen many threads regarding the same issues and have not seen any list for help,
This is an attempt to summarize all current & most common known bugs, in a way to prevent overloading this space while referencing the other threads that discuss each bug.
Its also useful to use this site's search using the ES2 filter, and of course, if your bug isn't reported yet (check Reporting an issue thread).

Common:

• Known typos
• Politics mechanics. (also check random voting thread)
• Battle UI ship name displays "name"22 instead of "name"2.

• Vision and ownership color don't change after capturing system.

• Ground battle bug [original thread]

• Can't move fleets.

Lumeris:

Vodyani:

• Invasions proceed against ground troops instead of Ark
• Leeching suddenly turns off

Sophons:

Cravers:

• On war status with enemy empire turns to positive.