When you are beginning primary fermentation it is actually beneficial to the development of your yeast culture to get as much oxygen mixed into solution in the must as possible. Later on, when primary fermentation is finished and you want to move the mead to a secondary vessel for clearing (and also for subsequent transfers either to additional aging carboys or to the bottles), you want to minimize exposure to oxygen since the yeast will no longer be using it and it will end up oxidizing the finished mead. So, oxygen early in fermentation is good.
Oxygen late in fermentation, aging, or in the process of bottling is bad.
The typical home meadmaker minimizes the introduction of oxygen into the mead by "racking," which is another term for siphoning without sucking up the lees in the bottom of a carboy, from one container to another. Racking disturbs the mead as little as possible during the transfer, and that results in the introduction of the least possible amount of oxygen into the must.
So when you are first mixing up the must prior to pitching the yeast, slosh away! You should also continue to stir the must while the first 1/3 of available sugars are fermented, as that will introduce more O2 that will continue to be utilized by the yeast. After that, slosh no more!
