Note: since GitLab 6.4, side-by-side diff view is available: see "pull request 5308".
(July 2013)There is no possibility yet to comment on each line though, only at the file level.
Daniel Sokolowski mentions in the comments that Per line comments are now supported (09/2014):
Your team members can comment on the merge request in general or on specific lines with line comments.
That still can help for code review activity.

6 years later, for GitLab 13.1 (June 2020):
Merge Request Reviews moved to Core
Originally introduced in GitLab 11.4 as a GitLab Premium feature, Merge Request Reviews allow merge request reviewers to:
- submit multiple comments at once,
- cutting down on notification noise for the merge request author, and
- allowing for a more cohesive and streamlined review process.

Since its introduction, we’ve re-evaluated its place in our buyer-based pricing model and as part of 13.1 we’re excited to announce this feature has now moved to GitLab Core.
See Documentation and Issue
With GitLab 13.9 (February 2021), you also have:
Request a follow-up review from a Reviewer
Merge request authors receive feedback from reviewers. Often, this feedback needs to be re-reviewed to make sure all issues have been appropriately addressed. As the author of the contribution, you need to communicate the need for a follow-up to your reviewer.
For reviewers who have already reviewed a merge request, you can now request a re-review. This request triggers a To-Do item and email notification to alert the user that you need a follow-up review of your contribution.

See Documentation and Issue.
With GitLab 13.11 (April 2021)
Add standalone comments to merge request reviews
When you’re reviewing changes, you may want to summarize your feedback, or comment on something unrelated to the specific changes. Reviews in GitLab only allowed commenting on the changes or replying to existing comments, which meant that other kinds of comments had to be made after submitting the review.
As part of your review process, you can now submit a general comment along with your replies or change-specific comments. General comments make it simple to provide feedback to the author and use quick actions to update items across the merge request.
Thanks to Lee Tickett for the contribution!

See Documentation and Issue.