Tim,
I had a similar problem a few years ago in 9.3 after excessive use of the SMOOTH tool in the "Advanced Editing Toolbar" on polylines in a FGDB. The SMOOTH tool creates geometric curves. I can't recall all the symptoms of the problem, but it would cause failures to simple merge editing operations (I'd get zero length for the merged feature) in the FC and any other geoprocessing I was attempting. No error report came up; just the output was negatively affected. Didn't try TRACING.
I first resolved it by running REPAIR GEOMETRY. I cannot recall if I found anything with CHECK GEOMETRY, but REPAIR GEOMETRY reported self intersecting lines and some null geometry that caused total glitches of the FC in other operations. Subsequently, I avoided the problem by running the GENERALIZE tool (also in the "Advanced Editing Toolbar") after using the SMOOTH tool on complex polylines, with judicious choice of the offset parameter in order to preserve the curvature of the lines, but as a simpler feature type. It approximates the geometric curves with short line segments and eliminated small loops that were only visible on screen at extreme zoom.
That didn't mean that I could not use SMOOTHed polylines (or polygons) or other true curves in the processing I was doing, but just that I had to be careful with the various true curve generating tools which apparently have potential to create weird geometry in complex individual polyline or polygon features that does not show up at the normal editing scale. If in doubt I use GENERALIZE with a small offset on complex curves that I need for some other operation.
See if REPAIR GEOMETRY works first and preserve your geometric curves; if that isn't sufficient try the GENERALIZE tool on the complex features (similar effect to exporting to shapefile and reimporting).
I'll be interested to hear if it works, and what sort of curves you were using.
Hardolph
