I have a question about how exactly to tackle the “errors”. The E4 and the E5 run in my area - if I jump to the next deviation, I come to Hallstatt.
From my point of view, everything is entered correctly in OSM. The path bends upwards in the aerial photo and the Strava heatmap is also clear. The blue line is called “OSM reference” - which reference in OSM? At least in JOSM I can’t find any other data in the OSM database behind the blue line.
Can someone explain how to “fix” this? 
Most often, when in “OSM reference mode” (contrasting with “GPX reference mode”), deviations are not errors. They are improvements that have been made in OSM, and that create a difference with the snapshot taken in the past.
That is why I do not consider managing these differences as a priority. Continuity issues (the vertical line, the red dots and the numbers besides the red dots) are much more relevant.
I think, when a route operator uses this monitoring tool, the snapshot reference allows the operator to see where mappers have improved the route, supposedly based on survey (or heatmap). Operators tend to have their own databases, maps, information site and/or GIS, so OSM is user input triggering changes in their systems.
The gpx-reference is for OSM-mappers to improve the OSM-route, based on a gpx which supposedly gives the correct route. This gpx could come from an operator, or traced from survey. So it’s the other way around.
I am a middle man between OSM and our national operator. I compare the gpx-file from the operator with the OSM route. All the differences are significant to me, because they require either OSM-route relation change or Operator gpx change, and sometimes both.
In all these workflows, verification by survey or survey reports (including heat maps) and viewing tools remain the most important issue.
However, first you need to have the relations complete and structurally sound. And for that, the enhanced continuity line in Knooppuntnet Monitor is a fine tool.
The continuity line of the relation editor in JOSM is not bad, but a) it works only when all the ways have been downloaded, and b) you see either the continuity in the parent superrelation, or the continuity of the child relation. Knooppuntnet gives both in one overview, with remote control links to load the problem in JOSM.
ok got it! Thanks for the direction, I’ve already started with the E4 in Austria.
May I can ask some followup questions:
How often is the tool updated?
What is the function/meaning of roles like “start4” or “end3”?
Are these sections? Can’t find anything useful in the wiki.
How to fix “forward/backward” problems?
Example: https://www.openstreetmap.org/relation/2069367
There is a roundabout here: Way: Badstraße (27450351) | OpenStreetMap
I really tried to switched the order in JOSM to fix the gap, but I can’t manage this. Any advise?
Thanks!
Every hour or so I think.
Welcome to the club 
I believe these might be attempts at structuring the route into segments or main+alternative parts.
There’s a ticket in the Knooppuntnet github but I’m not sure everything is clear for anyone on this topic.
