Reviving the thread.
I have had similar problems with Abiword in Gloria-main, but not in previous Linux Mint versions.
The screen fonts were very thick (thicker than the normal 'bold') and, as I typed, each letter was underlined with a short thick bar - just as in the original post in this thread. Deleting the letters with <Backspace> still left the bars. They only disappeared when I pressed <RET>. Then they started again on the new line. The cursor was a very think bar and it didn't blink.
As an aside, the OpenOffice screen fonts were very poor as well.
I spent a considerable time trying to find the cause, but couldn't. I tried everything suggested here, including downloading and installing Abiword again. I started off with my standard font settings, and then tried others. All to no avail.
So, wondering if it was something to do with one of the updates, I ran the live CD of Gloria-main, and downloaded Abiword. Exactly the same problems.
Next, I ran the live CD of Gloria-XFCE RC1 and downloaded Abiword again. No problems! Abiword ran perfectly, as it has done in the past.
OpenOffice fonts were all excellent.
So, finally, I replaced Gloria-main with Gloria-XFCE RC1 on my hard drive, did all the upgrades, and installed Abiword.
It all looks and runs great, and I am a very happy XFCE user! But it's rather a drastic thing to have to do in order to get a program to run correctly and for the fonts to look good!
Just thought that this may be of interest to someone.