I actually think the movie does a pretty good job of showing the relationship between the characters and staying true to the plot of the novel by having Paul Baumer narrate the film like he narrates the book.
Think about the opening scene where the soldiers are lined up in a trench. As the camera comes to a close up on each one, Paul is narrating information about each character. This not only serves as a brief introduction to each character, but it provides necessary background information. Additionally, it shows that Paul knows his comrades and friends. It also shows that he knows each one equally, despite the fact that he went to school with some and others he met in the war.
Also, if you review many of the scenes of "downtime" when the characters are not actually fighting, you'll again be provided with Paul's narration through flashbacks to school, flashbacks to boot camp and training, and also present tense versions of conversations these men had with one another when the stress of combat wasn't immediately present. Even though the film is a little bit older and the special effects do not mirror what is being done in film today, this is one book-to-film adaptation that maintains much of the original plot and tone portrayed by the author. The relationship between Paul and the other soldiers in the film are strikingly similar to his relationships with the same characters in the book.