My tuppence worth: I drove my Elan as a daily transporter for over eleven years, doing the "Fix-I-Go" repairs as necessary. When it's been gone through (soon, I hope) I'll start using it again as primary. Too much fun NOT to drive it, and ~yes~ they are that addictive if you like spirited cars instead of the insipid lumps currently being passed off as plebean transport.
As for the "trouble spots" I'd say the water pump is the "usual suspect". Change it every 40K miles. I HAVE done it with engine in situ (once even did a Europa T/C this way... NOT recommended!) without removing the head: pan loose, lots of RTV. Better to pull the engine. Donuts are a challenge, as is the rear suspension/bearing hubs, but not horrible with access to an appropriate spring compressor and good hydraulic press. The reason it sits now in the garage: frame damage (tangental crack) at the lower diff stabilizing points. Body off to commence after first of '06. As stated above, the +2 is a much more civilised daily driver but due to the added mass the driveline seemed to need more attention: never had a catastrophic donut failure in the Elan, but did in the +2. Also snapped a stub axle, so uprated to the more robust units Dave Bean supplies. Front right upright in the +2 has broken due to rust worms, it gets the "treatment" as soon as the Elan is back on its' feet. I ~MISS~ driving the Elans as daily cars. The Alfas are okay... but there's nothing to take the place of an Elan IMHO.