I have been using Dansco albums (Whitman and Dansco albums are similar) since 1984 with no ill affects.
If the plastic slides are rigid, then they should be okay. The bad plastic for coins is
soft PVC. PVC itself it not bad, but the plasticizers used to soften it is what leaches out onto the coins and causes the green slime. If those slides have a rainbow sheen and a greasy feel, do not use them!
I do not think Whitman would use anything other than rigid plastic. There is no need for soft plastic in this type of album (unlike the old Harco albums or the 2x2 vinyl flips).
Anyway, I know Just Carl has used Whitman albums for many, many years, so I would take anything he says about them as the final word on it! He will see this post eventually...

Edit: I forgot to add, where you store the albums is the important factor. Keep them in a climate controlled environment and they will hold up well!

Edited by jbuck
11/01/2008 10:16 pm