I agree that moving the parliament between two different places seems dumb. If it's cheaper to remain in one place then they should do that.
As for corruption and misuse of funds, maybe that does happen. Maybe the solution though is to elect better politicians to run the EU, rather than leave the EU.
I've thought in the past that maybe the EU should have a directly elected president, in addition to EU citizens voting for European parliament members. This might allow for more democratic accountability of the EU. Someone might run for the presidency on a platform of stamping out misuse of EU funds.