There are two aspects of the question: shouldShould you try to find the necessary information (papers) to do a good review? andAnd should you contact the author of the paper you review to ask for other sources written by that author?
It is clear that you should attempt to gather all information you deem necessary to perform your task as reviewer. Since journals typically only accept published materials to be used for sources (with the possible exception of unpublished data or personal communications) you should be able to find such information given some time and work. That said, I doubt that many would keep a review on hold just because they have not been able to find a specific source unless that source is absolute key for a critical (in the negative sense) aspect of the paper. It is, however, possible to inform the editor that you have not been able to check up on this particular aspect since you are unable to obtain a copy of the paper within a reasonable time. Although it is always possible to purchase papers from publishers, I do not think we consider such actions within ththe expectations placed on a reviewer.
Now, the second aspect about contacting the author for more information should be handled with care. As an editor, I would first of all want to be aware of such communications. Peer review is based on an objective evaluation for materials and although a simple request is not likely to change much it simply removes part of the desired distance between author and reviewer. One solution to this, which I would prefer is for the reviewer to contact the editor and ask for the material (from the editor or from the author through the editor). It has not happened to me that i have received such a request but I would not consider it other than a positive. I would also add that if a reviewer I slackingis lacking some key piece of information (as stated in the previous paragraph) I would greatly appreciate knowing about this weakness in the review. Given such information, I could, as and editor, add key comments of requests to the author to improve the paper in some respect.
As a side-point, I would like to add that some papers that totally rely on other previously published on, for example methods and error discussions, should include enough of a summary to make the paper stand on its own in its entirety. It is thus possible to request a major revision with the explicit wish to see additions to the paper to remove the necessity to have to read other papers for key aspects. I fully realize the delicate balance in such requests since no-one is striving for excessively long publications.