Regarding your "also", a couple points:
1) Your IP is typically not widely-known to other users. If I say "123.234.123.234 is an idiot!", nobody will know who I'm talking about.
2) A lot of people (read: "the vast majority of home users") have dynamic IP addresses and this is well-enough-known that I don't think you have to worry about it hurting your reputation even if you do get someone else being a twit from your former/future address.
3) If your concern is more legal rather than simply public reputation, ISPs keep logs of who has what IP address at which times and, if they need to track someone down, law enforcement will request those logs to see who had that address at the time of the crime, so there's no danger of you getting busted for what someone else did just because they did it using an IP address that you had previously been on.