Okay, so I did some testing to try and figure out why and when this error is occurring.
I actually had some trouble getting the error to happen again. The models I have been testing only have the dissolve process without any dissolve field selected. I have found that the error only occurs when attempting to make multi-part features. The model will function as if the "Create multipart features" option is not selected. The result will dissolve all overlapping polygons, but each will be an individual feature instead of a singular multipart feature.
I tried the simple process in modelbuilder and a python script, attempting multipart and single feature outputs. The error occurred in both modelbuilder and python multipart outputs. However, the error only occurred when I had either several browser windows open (Chrome) or had any streaming video or audio at the time. I tried to run the dissolve outside of the model during similar browsing activity, and it worked perfectly. It even worked when I opened up 8 videos simultaneously.
I'm running Arc Desktop 10.2 SP1 on a Windows 7 - 32 bit, 4 GB RAM, Core 2 Duo E8400 3.0 GHz processor, which exceeds ESRI system requirements.
I hope this can help you at least duplicate the error I am having. Thanks for any help or information you can give me about the situation.