Okay, so the automatic landing system is an issue - isolate it from the main network (might be hard if needs input from Nav, but there are ways) and look for the next issue. Or limit its ability to accept input (do something about that buffer overflow trick... who wrote these things - Microsoft?). Or turn it off during periods of Cylon contact (have to park or land manually during battles). They need those systems.
The rest I agree with. But Caine is a babe... and I'd want to be on her crew (as of Pegasus, anyway).
There are ways, but here's the main problem: how do you find out you've shut down every way the Cylons have in? Gotta get near Cylons and hope. It's established that part of why Galactica is totally unnetworked is that Adama is kind of superstitious about it, Galactica is absolutely unnetworked because it's his ship and he said so. From what we can tell Caine managed to figure out the weaknesses in the network and turn them off so Pegasus is safe, but Galactica is Adama's ship and he refuses to allow any networking at all. Who wrote those things included at least one Cylon remember (or at least she had fairly unlimited access to the source code for finding weaknesses), so they were probably pretty heavily infiltrated. Apparently they don't need the systems too much, at least Galactica doesn't, it's kind of one of those technology crutch issues 30+ years ago people didn't "need" cellphones, now 3/4 of our society wouldn't know what to do with themselves without one, Adama refused to allow ships he commanded to be networked so he's adjusted to a nonnetworked ship, even Apollo doesn't like it. IMHO that's one of the reasons Adama didn't move his flag to Pegasus, too much network for him might as well give the ship to somebody that actually likes the things.
Caine was a babe, but she had issues.