As for the brakes, the rear cylinders have a tendency to seize.
Can be checked when you remove the drums.
Front brakes aren't great by design. But if you behave a bit on the road [;)] and with decent pads they should be adequate to give you time to accustom to the car. But do check and clean them also.
Oh and bear in mind that the standard front pads are the same as those of the later Mini's (from somewhere in the 80's on). Might be much cheaper ...
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<font color="blue"><i>1981 TR7 FHC Sprint (better known as 't Kreng)
1981 TR7 DHC (not very well known yet, but back on the road)
Also a 1980 TR7 DHC, 1980 TR7 DHC FI, 1981 TR7 FHC
http://tr7beans.blogspot.com/</i></font id="blue"></center>