It sounds like there is more than one suggestion in these comments that could be called a "logging feature." My opinion is that RayGun is Exception Tracking software and should continue to focus on exception tracking, and not logging. There are plenty of services that already do focus on logging (i.e. Loggly, PaperTrail, etc.).
With that being said, I'm not sure if this is what someone was suggesting, or just my adaptation of it, but it could be relevant to log messages that would be included in some kind of "log output" section of an Exception if and when it does occur. The question is how you determine where that log starts. In a web application it would be simple enough - start it with the request, or in the case of a background job, start it with the job. In some other long-running application, it would be more difficult to determine how much of the log output to include. The log data could be ridiculously long for a long-running application, and how do you decide how much of it is relevant? Perhaps it's a stack-like structure rather than a simple sequential log? Where the log data from each iteration of a loop replaces the data from the previous iteration?
In any case, I agree with the original staff post that it is too big to be simply bolted on to the side. I'd prefer not to see a half-implemented logging solution in an Exception Tracking application. I would like to see either a very focused implementation, relevant to exception tracking (as above) or a full-featured logging solution that integrates with, but is separate from the Exception Tracker.