Interesting thread on ESRI Forum participation; it deserves it's own thread.
As for the awful and wonderful trace tool, here's some suggestions when you have problems.
1. As noted, use classic snapping.
2. If you have a lot of features that the trace tool can switch to, turn off those you don't need. This also gets rid of their vertices when starting the snap.
3. Watch your snapping tolerance. It typically is in pixels, and hence how fine grained your screen and zoom in scale are for the work at hand matters every time you click/touch.
4. Zoom in to keep the line from jumping features; you can use the < and > to zoom back and forth without having to change your tool. If you have to switch to the pan or zoom, you have to re-click the tool to get it back to work. See 7 too on this.
5. If the lines or edges you trace have gaps, even at a fine scale, that may cause the tool to fail. It seems odd but sometimes the trace tool will jump gaps, and it always seems to be to another feature when it does that, but never in the one you are tracing.
6. Whether it is a real gap or not, sometimes you have to switch to the straight segment, click/touch, and then restart the trace even if you didn't really create a straight line segment.
7. If you are tracing features with a very large number of vertices the trace tool can slow down; it requires a fair amount of processing, so your computer matters. A series of traces zoomed in might work. By that I mean you zoom in, run your trace to cover part of your work, click/touch to stop, pan, click/touch to restart (and get a fresh cache? of the vertices, and then keep doing this until finished.
8. Sometimes other tools just work better. If you have ArcGIS Advanced/ArcInfo the Construct Features taking into account existing features, or the split tool, work great. If you have lines to match, a simple copy and paste may be in order.
9. If you are using the trace tool you are using it as part of another tool like autocomplete, and there are known issues with it in some versions of ArcMap.