When a person is eating meat it is forbidden to have milk on the table (and vice versa), because you might end up eating them together by mistake (שו”ע יו”ד פח:א). This halacha applies whether there are two people eating together, one eating milk and one eating meat, or one person eating meat by himself and there is milk on the table. If one eating alone mistakenly had both on the table, they should remove the one that they are not eating. This prohibition only applies when eating, but if you are just putting food down without the intention of eating it, it is permitted to have meat and milk on the same table. For example, it is permitted to arrange a platter of meat or to place hot meat to cool on a counter, even though there is dairy food on the counter.

The prohibition of meat and milk on the same table applies to actual meat and all milk, as well as to food cooked with meat or milk. The prohibition does not apply to non-dairy food cooked in a meat or milk pot. Other prohibited foods such as non-kosher meat may be on the table when you are eating. The reason that other prohibited foods may be on the table is that we are always careful about those foods since they are always prohibited to us, as opposed to dairy and meat which on their own are permitted. Therefore, the possibility exists concerning meat and dairy that one might mistakenly eat from one while eating the other.