Okay, I've found the cause and the solution. Why it's happening can only be attributed to Lion. Only since Lion have I ever had any issues with iTunes.
I've had three issues when adding Mp3's to iTunes. Sometimes they all occur, sometimes one or two, with each file. It occurs with the two types of import, whether you "Add to Library," or simply highlight multiple songs from an Mp3 folder and double-click.
The issues are:
1. "Determining Gapless Playback Information, " every time I open iTunes.
2. The songs affected by the above issue also sometimes do not play in their entirety and skip to the next song.
3. Also, while playing the affected songs, if you attempt to skip ahead (near the end of the song) by clicking the progress bar, it will not jump to that part. For example, if three minute song is currently playing and it's at 1:09, and I try to click around the 2:45 mark, it will only jump ahead to the 1:50 mark. If I click the end of the song repeatedly, it keeps jumping only to the 1:50 mark. Once I stop, it will continue playing beyond that, however.
The crazy, simple, PITA solution is to add the Mp3's one at a time. I just tested it. I had about 68 Christmas songs (three folders, three albums) I added to my 65 gig iTunes library yesterday. When I opened iTunes this morning, I had all of the above issues with the songs, even after closing and reopening iTunes. I deleted all 68 and added one at a time. After the first two, I closed iTunes, reopened, and there were none of the above issues. Now all are added with no issues. I double-clicked each Mp3 to add it.
It would be nice to know if others had the above issues in conjunction with "determining gapless..." and/or test this solution. The issue may simply be due to adding multiple files at once. If this is the case, Apple could be notified as to how the issues are occurring, then they could figure why.