"the Db returns to a D on beat 1 of the new measure even though it is slurred with the measure before"1. Flat the D on beat 1 of the new measure. Don't worry about the flat displayed in the new measure. It will disappear when you have finished step 2 (you may have to move to another measure before you can see that the flat is no longer displayed).
2. Use ties instead of slurs.
Slurs are Smart Shape Tool items that are intended for phrasing (legato).
Ties are Speedy Entry Tool items (and Simple Tool items). In Speedy Entry a tie is entered with the = key.
You don't mention which version of Finale you are using.
In Finale 2002 the Speedy Entry Tool keys for flat, sharp and tie will work on the note just entered, even if you have jumped to next measure.
For earlier versions of Finale, try this trick (assuming that you want a tied 8th note D flat in the end of the first measure) in Speedy Entry Tool:
1. Enter the D as a 16th.
2. Hit the - key to "flatten" the D.
3. Hit the LeftArrow key to move the crosshair back onto the D flat.
4. Hit the 5 key to turn the 16th into a quarter. Now the alert "There Are Too Many Notes..." will appear.
5. Click the option "Move the Extra Notes to the Next Measure", and hit Return. The Speedy Entry rectangle will jump to next measure where the crosshair will be on the first note:
an 8th note D flat.
6. Hit a number key to give the D flat in the new measure the value you want, and make the crosshair move to the right.
This trick can be very handy for entering a long sequence of tied whole notes!
Peter