The MK4 Jetta came with two versions of floor mat retainers.  The first version uses a peg, push-on, style retainer.  The second version uses a twist lock retainer.  Im not positive when theses changed, I believe I read 2003 somewhere, but my 2004 had the twist lock style.  I ordered a new set from IDparts.com and they came with the peg style.  After some searching I learned that they were easily swappable, and go for roughly $9 online.  Luckily I have a spare set of mats from another jetta with the correct clips.  Below are some photos of changing them over.

Remove the clip by carefully prying the bottom clip away from the top clip.

The same can be done for the ones you are replacing.

After that, its as simple as aligning the two clips and pressing them together.  I found that pressing them against the floor was a much easier way to get them connected.  The rubber is much thicker than the carpet mats, and it takes a bit of effort.

And thats it.  I have listed the VW part numbers below.

Floor Mat Retention Clips (Round):  3D0061493A041

Floor Mat Retention Clips (Oval): 3D0061795B41

Monster Floor Mats (Round): 1C1061550041

Monster Floor Mats (Oval): 1C1061550A041