To reproduce this problem do the following.

In Preferences > Messenger > Desktop Contacts, enable "Alter settings based on contact's status [Change transparency]
Again there, set the transparency level to 0 % i.e. opaque.
Now show a non-Online (busy, away, offline) contact on your desktop.
Hover your mouse over it, it will not become opaque (almost opaque*) and it will stay transparent.

If you enable the custom transparency option for such a contact and set it to opaque, it will reproduce the bug either. I think this bug is valid for online contacts too but we cannot see it by eye because because they're online, the desktop contact windows are already fully opaque before hovering mouse on them.

If it is a little transparent like 1 %, then it works correctly.

*I noticed that it is still not fully opaque on mouse over; one can very hardly see a black writing behind a white background

I also noticed that, regardless of what you selected for the option "Alter settings based on contact's status" in Preferences, if the desktop contact window is transparent, it doesn't become opaque when you drag a file, text or link to it. It stays as is.