I get an error when using an R function that I wrote:
Warning messages:
1: glm.fit: algorithm did not converge
2: glm.fit: algorithm did not converge
I gave this answer to a more recent question, but am adding it here for completeness.
Personally I tend not to use functions to debug. I often find that this causes as much trouble as it solves. Also, coming from a Matlab background I like being able to do this in an integrated development environment (IDE) rather than doing this in the code. Using an IDE keeps your code clean and simple.
For R, I use an IDE called "RStudio" (http://www.rstudio.com), which is available for windows, mac, and linux and is pretty easy to use.
Versions of Rstudio since about October 2013 (0.98ish?) have the capability to add breakpoints in scripts and functions: to do this, just click on the left margin of the file to add a breakpoint. You can set a breakpoint and then step through from that point on. You also have access to all of the data in that environment, so you can try out commands.
See http://www.rstudio.com/ide/docs/debugging/overview for details. If you already have Rstudio installed, you may need to upgrade - this is a relatively new (late 2013) feature.
You may also find other IDEs that have similar functionality.
Admittedly, if it's a built-in function you may have to resort to some of the suggestions made by other people in this discussion. But, if it's your own code that needs fixing, an IDE-based solution might be just what you need.