Hi! I recently switched provider from Telia to Halebop, which is basically a low price alternative within the same company. As with Telia I get a private IP in the 10.x.x.x space. The problem is that i occasionally connect to home via PPTP, which worked fine with Telia, but not with Halebop. Strangely Halebop uses Telia's network and I even have the same APN as I did with Telia. I've been in contact with support and they can provide me with a public IP to sort the problem. How would this affect security, as opposed to being behind NAT?
And yes, I know there is an AndroidQuestions forum, but not very much seem to happen there, so I turn to the competent collective here instead

It essentially opens you up to attack vectors and port scans which were not possible in the public avenue when you're behind a NAT. If you have a rooted phone I recommend you install DroidWall which is an iptables firewall on android. Visit a website like ifconfig.me or even on your home wifi and run a simple port scanner on your phone to see what ports are open (nmap for e.g. can do a quick port scan and a deep port scan). Sometimes the apps installed on a phone open network ports which can then be connected to. In this instance DroidWall would help mitigate most of these security issues.

I'd like to point out that while on wifi or WAN your phone is just as vulnerable to attacks like this but they carry a little more weight of concern because you have a publicly routable IP.

DroidWall is discontinued. Android Firewall is a fork that is actively developed.