Hi Megan,
Acrylic manufacturers tend to specify a tolerance for sheet thickness, which can vary by a fraction of a mm. That can be problematic when you are slotting material in at right angles,
because it will sit proud or below the surface of the other sheet if there is a difference, but that's not what you are showing here.
Additionally, the laser's 'kerf' needs to be accounted for by the laser cutter. The kerf is the width of the cut that the laser makes in the material. Ideally, your laser cutter should have done a test cut and measured the item cut using digital calipers, in order to calculate the kerf, and then entered a kerf offset in the laser software, in order to account for that kerf. For example, if I cut a 40mm square, it might come out at 3.88mm - normally such a small difference may not be significant, but when it comes to slots, it definitely will. So that 0.12 needs to be factored in to the cut...how this is done depends on the laser software being used.
Kerf may not be the issue here, but it's worth knowing about...