Vivian, Do your missing places have numbers? If not then you need to run Utility => Check with _only_ the Event and Event Links checked. Then click on Repair. This process will give all of the missing places a number which will match one place per number.
Then go to View => Event List => By Place, The missing places with numbers will be at the first of the list. If you select one and key F8 it will bring up the event with that missing place. The trick now is to remember what that place should be when you do select the place name field and key Shift-F6. This will bring up the Place Name screen. Change the number name to the real name. This will change all the events that need this number.
Key F4 to go the next missing place number. Repeat.