Cortinas are well known for having electrical problems, particularily with the dash. Also they are fairly average in the handling department, especially the 6cyl models, terminal bodyroll and understeer when pushed hard. A good set of swaybars, shocks and springs are a must IMO.
The single rail gearboxes are different in Cortinas to Falcons (shifter comes up in different spot) so be aware of this if buying one second hand. I think you can interchange the rear extension housings between the Falcon and Cortina boxes so all is not lost if you pick up the wrong one. The syncro rings tend to go, especially in second gear if you give it a hard time and the thread on the shifter where it goes into the gearbox wears out after a while (the gearshift can come out in your hand if you are doing a racing change!). You can get around this to some extent by putting a radiator hose clamp around the metal tabs on the bottom of the shifter. I think there was some mob doing some trick aftermarket shifter for them but they were arounf $5-600 (can't remember who or where - if interested try somewhere like Mal Wood in Qld).
Also, if you do excessive burnouts you can rip the rear upper control arms out of the floor. I used to do heaps of burnouts in my turbo 6 TD Cortina and never had this prob but I have heard of others that have.
For $350 you really can't expect too much.
Another thing to watch out for if you have a vinyl roof is for rusting under it. Best thing you can do is to get rid of the vinyl IMO.
Hope this helps.
You know, somebody actually complimented me on my driving today. They left a little note on the windscreen. It said, 'Parking Fine.'So that was nice.