Sounds like you need to start moving this stuff out of house. http://Dyn.com or http://www.zoneedit.com/ for dns, http://www.google.com/apps/intl/en/business/index.html for mail, webhostingbuzz or whatever for your website.
Honestly for how cheap all this stuff is it's almost worth it to do it out of your own pocket just for the peace of mind.
OTOH you could get busy on setting up a split horizon BIND configuration. I assume your ISP provides you with a static IP, and you have NS entries setup with your registrar already? Did the previous admin contact the ISP to setup reverse DNS?
Over the years and on different projects I have used UltraDNS, ZoneEdit, DynDNS; all of which were easy to use. UltraDNS seemed to be most scalable if you have a huge project with a lot of lookups. ZoneEdit is free until you get to a certain number of records.
Currently my projects are hosted at Linode, and they provide a BIND-based DNS manager that is both easy to use and scalable enough. You can use their gui frontend or work on zone files directly if you know what you're doing.
We're working on revamping our entire DNS offering and that's one of the things we're considering, but we don't currently support dynamic DNS. We'd suggest partner site Zoneedit - they offer a couple DNS zones for free and include Dynamic DNS as an option.
I find zoneedit to be a fairly simple, good option - first two zones are free, after which each zone is 1$ per zone per month.
It supports dynamic dns without any subdomain bullshit - I do not like the idea of sharing my domain.
give http://www.zoneedit.com/ a shot. i've used them for a few years without much issues. my free account is still on the legacy system which is still waiting to get ported over; i cant really comment on the new system much.