Coverages have a 500 maximum vertices per feature, then they are "split" with a "pseudo" node (two lines into one node). If auto split, the -ID ("dash Id") will remain the same. Just an FYI, one line into a node (eg an end point) is a dangle node....multiple lines to same node, makes it just a node, by definition.
i haven't used the ArcGIS Desktop tool much for coverages, but the best, most reliable way I found when I was moving my coverages to geodatabases was to take advantage of the coverages "REGION" features. The region features let you group or associate multiple features by common attributes (with tools) or by manually selecting features in ArcEdit. You can use the same feature in more than one region feature. Clean topology (i.e., nodes that connect, lines that don't overlap, etc.) is still important, and using the BUILD command in ArcINFO Workstaion (with the property feature type as an argument) was important. CLEAN could also work, but could eliminate features or adjust vertices within the fuzzy tolerance if not careful.
With REGION features in a coverage, you could actually have multiple representations, or REGION feature classes, of the different features types (point, lines, polygons) as separate displays from the same underlying geometry. This was very powerful.
The semi-equivalent data management style in a geodatabase would be a dataset and feature classes with topology rules in place. We used our REGION features, which were mainly based on polygon features, from about 27 different coverages, and where able to rebuild the polygon features into three gdb feature classes with topology. I realized after multiple tests that mixing the arc/line and point/label/attribute REGIONS with the Poly regions in the topology didn't work, but all can be re-created with custom scripts to rebuild what I had in coverages.
more than you probably were asking, but it may help if/when you start moving from coverages. I was a hold out for many years and had to wait until the topology rules were adequate, and a projection bug was fixed (which happened with the release of 10.0, so a few years back now).
So, bottom line, I'm not 100% sure about DISSOLVE and more, but the FUZZY tolerance (which can introduce fuzzy-creep), the 500-vertices limit, other possible "tolerances", etc can effect coverage processing. Instead of DISSOLVE, try creating REGION features that is very powerful and will not change the underlying geometry. Once the geometry is clean, you can convert the REGION features to gdb feature classes. My recommendation.