1) The ovens that are found in most homes today are manufactured in such a way that their openings are closed and their doors are hermetically sealed to ensure that no heat escapes and that the heat is evenly distributed to all parts of the oven.
While items are cooked/baked in the oven, the heat and the steam that escapes from the food being cooked/baked gets absorbed into the walls of the oven. (Sometimes this can even be visible to the naked eye in the form of dried gravy, which get baked onto the walls over time) and can then be transferred onto other food in the oven. (See Darchei Teshuva Siman 92:164 and Shu”t Minchas Yitzchak Vol. 5 Siman 20:10)
Therefore, the usage of this oven for uncovered meat, dairy and Parve simultaneously is prohibited.
Furthermore, even if the oven is not used at the same time for opposite food classes, but is used consecutively, it is also problematic if the foods are uncovered, and surely L’Chatchilah it should not be done.
2) Although many ovens today have vents that are made to remove the steam from the oven, most Poskim do not consider this significant enough to override the problem of steam from one food class in the oven mixing with food of a different class, and thus keep to the ruling that if both classes were cooked in the oven uncovered simultaneously or even consecutively, it will render the food problematic.
In the event that food was cooked in any of the aforementioned situations, a competent Rav must be consulted for a ruling.
(See Rama Siman 108:1 and Igros Moshe Yoreh Deah Vol. 1 Siman 40. See also Badei HaShulchan page 211. See also Shu”t Minchas Yitzchak Vol. 5 Siman 20:8-13)