Whilst Ubuntu say it's "Certified for Ubuntu" 12.04 (which Mint 13 is based on):http://www.ubuntu.com/certification/hardware/200912-4897/
There seems to be some confusion over the ethernet adapter and card reader from Ubuntu Friendly entries:https://friendly.ubuntu.com/12.04/Dell%20Inc./Inspiron%201545/i:C4I:BrLDXp:Jw8:BEG:LA:BEip:E2z:BYQ:M:BEi/
Where 2 entries say everything works .. but 3 others say they've had issues with the ethernet adapter and card reader .. one even suggests the USB controllers don't work (but I'm sure that's wrong).
A quick search around the internet only seems to suggest the need to install bcmwl-kernel-source
to get the wireless working .. which may be difficult if the ethernet adapter doesn't work, so it may be worth having a "known to work out of the box" USB wireless adapter handy just in case.
But easy enough to test the hardware compatibility with a LiveCD/LiveUSB anyway .. so probably a good idea to test the ethernet adapter works from a LiveCD/LiveUSB before installing