1989 Oldsmobile Cutlass Supreme SL water pump
 

It has been a little over two weeks since I bought my Cutlass. I was told by a certified mechanic that my water pump needs to be replaced along with a couple of other minor things. I start the car periodically and drive it around so it doesn't get funny. I've noticed that some smoke is coming out of my radiator near the cap. This happens if I run the car for 30 minutes. I do check my engine coolant level before and after I run my Cutlass. The digital dashboard indicates that my engine isn't running hot and that my coolant level is not low. Should I trust myself or the dashboard and why would the radiator start smoking all of a sudden? This has been going on for over a week. Please let me know. :)

Is it really smoke or is it steam from the radiatior cap not sealing? If the cap isn't sealing, you can get a new one cheap at Autozone or a similar car parts store, and you should even if it doesn't overheat.
If the water pump isn't leaking, and the car doesn't overheat, why did the mechanic say you needed a new one?