When trying to move the map using set_center to a location close to the
current location, only the markers move, and the map doesn't.

The location of the markers will become incorrect.

If the distance from the old center to the new center is large enough, the
bug does not occur.

A test case: http://bliin.com/util/test_setcenter.html

The javascript in there should be self explaning, but here is the relevant
code:

<a href="javascript:center(52.44,4.00);">A. SetCenter 52.44</a>
<a href="javascript:center(52.45,4.00);">B. SetCenter 52.45</a>

<script>
  function center(lat, lon) {
    map.set_center(new google.maps.LatLng(lat, lon));
  }
</script>
 
Hope this helps,
Tomas 
bliin.com