common problems with pumas (not only puma but also mk4/5 fiesta as essentially same car.
rusty/rotten rear arches and sills, sometimes a-pillars too.
worn wishbones
worn anti-roll bar bushes/link arms (wishbones and roll-bar/links generally show as clonking over bumps and worn front tyres)
sticky heater control valve/temp control. stays either hot or cold. if cold try unplugging it, it should heat up, if hot then either valve is sticky (can be rebuilt) or faulty control dial.
DONT EVER LET THE OIL RUN LOW!!! it will very quickly cost you an engine. rebuilding is possible, but expensive, as are second-hand engines. a common trait with the zetec-se engine.
rear beam bushes,
check cambelt. 80k or 10 years whichever is sooner!!!
faults with tailgate electrics due to contacts in tailgate/boot lip.
clutch slave cylinder (always replace when fitting a new clutch (its so much easier to do then).
these problems are mainly general wear and tear items after lots of use/abuse, but if looked after pumas are pretty good and reliable and cheap if they do go wrong.