For the most part I cannot foresee a scenario for overlaps but we all model the data differently with different events so there might be valid reason for your data.
For gaps, are the gaps supposed to be there? For instance you have an event for curb and gutter, you probably should have gaps. If your modeling pavement type, there probably shouldn't be a gap in pavement type.
Based upon the event, how you model your data and what your temporal expectation is you can change the from/to measure in the table to fill the gap or remove the overlap. You can do this with the 'select by attribute tool' in Event Editor or use a third party tools. Additionally if the area is really bad I might retire all the records with the same from date creating a begin record using 'select by attribute tool' in Event Editor and then reapply new data with the same from date over that area with 'add linear events tool' in Event Editor. This method can help ensure that the temporal data is clean as well as opposite to just using 'add linear events tool' in Event Editor over the route to fix the area and retiring the bad data.
Unfortunately I think when you are down this far in the QC fixing it is a route by route, event by event type analysis and fixing, there are no clean bulk fixing because what ever method you are using it has been my experience it is only the correct method half the time.
Hope this helps
