Is it OK to not use place mats or a tablecloth for Milchig or Fleishig, on a glass table?
Any time a hot food item or a hot pot that is wet on the bottom (or if the table is wet) is placed on the table, it potentially transfers its taste and status to the table.
For example, a hot Milchig food, etc. makes the table Milchig. If the same thing will subsequently be done with Fleishig, there will be an issue.
Therefore we must always ensure that the table is covered when hot food is served.