There are a few tools that will automatically retrieve BibTeX-formatted references from MathSciNet. BibDesk is offered with TeXShop, but only works on a Mac. Are there similar tools that work for Unix/Linux or for Windows? There are a few applications written as stand-alones that get the job done:
mscget (requires python), bibupdate, bibget (a shell script).
JabRef can retrieve references from a number of archives, but MathSciNet is not listed among these resources.
Some potential tools are mentioned in this answer to What are good sites to find citations in BibTex format?, listed under "Reference managers that allow BibTeX export/import". MathSciNet is not included among the archives covered, although it is mentioned as a resource from which BibTeX-formatted references can be downloaded manually.
Note: I work for Mathematical Reviews / MathSciNet.