My Tips :I aint an expert, but i do manage to accomplish a few of the Mole Missions, except Fight Club (I hate it, therefore never takes part in it)
Suspected Car :Well, this is what i do. Once this mission flashes on the screen, i try to respawn as the character nearest to the vehicle.
StreetRace :Best ride for a race is Infernus, Buffalo or NRG. And as explaind by Wayne, never get out of ur vehicle during a race, or u.ll get busted automatically and end up in prison cell. And whats worse, if there r cops around u, each of them earns $10,000., so beware, dont try to hold a charity show here.
Moneytill :This i think is one of the easiest missions. Its only in LS, and its mostly at the 24/7 store and some other. Its hard to believe, but a BMX is ur best ride for this mission. I'll explain the reason why :
1. No worries about cops shooting off ur tyres
2. U can jump off and make quick escapes
3. No worries of refuelling.
4. No need to repair as it will never blow up.

But the most important of all, never forget to lock ur vehicle, unless u're planning on escaping on foot., which is obviously a bad idea.
PS : Psssstttt !!! Dont tell anyone about these tips.