Is there a way for students to view each other's assignment submissions?
not in the standard assignment module, no, but you could use the Workshop module which is designed for peer assessement or you could simply get them to upload to a forum.
Thanks. I think that I'll try the forum. Can another student actually comment of write directly on a fellow classmates document?
They can comment on another students post but they cannot update or edit another students post.
In 2.4 you can use a group assignment for this (it's an option when creating the assignment). Students share a submission between members of the group and all can update/comment.