Minecraft wiki entry for Best_biomes_for_homes, associated text: Somewhat inconvenient to build in unless an area is cleared. (But the player gets a lot of wood in the process)
Trees obstruct visibility.
It is difficult to recognize any one section of the forest, which can be bad if you get lost. (Of course, the player can always ascend to the treetops to figure out directions.)
Passive mobs can be hard to find due to the mass of trees around.
Hostile mobs are surprisingly prevalent here depending on how dense the forest is. Skeletons can shoot you from around corners, creepers can sneak up from you from behind trees, and undead mobs have plenty of shade to shelter in during the day.
Hard to run through due to the high amount of trees blocking your path. Also, horse riding here is near impossible, as suffocation in the trees is likely and hard to avoid without carefully traveling at speeds lower than simply sprinting without the horse.
Fire and lightning strikes are a major issue here as they can potentially start huge forest fires.