Your hosting provider will hold you responsible. If they keep getting abuse reports because spammers use you URL shortener in their e-mails. Hosting providers (including dedicated servers) do not want to be blacklisted by popular spam lists.

Absolutely not - there's no reason you can't implement black listing or whatever. I can guarantee that there are URL shorteners out there that redirect to porn.

In some jurisdictions you have to fight hard to prove you are not if it comes to anything. That fight could be costly.