How do I fix inconsistent boundaries?

Note that administrative boundaries are likely to be in a relation, i.e. you will have multiple ways that together form the boundary.

To solve your problem, for the first boundary:

• Identify the node in the boundary where the boundary should start to run along the coast.
• Split the way at that position, if that position is not already one where two separate ways meet.
• Identify the node where the boundary should branch inland, away from the coast.
• Split the way at that position (as above). If the whole boundary is one circular way, some editors may require that you mark these two nodes at once and then execute the split.
• Now delete the boundary way or ways that is/are supposed to coincide with the coastline.
• Similar to the above procedure, identify the nodes in the coastline where the boundary should join and leave the coastline, and split the way unless it is already two parts.
• Now drag the admin boundary node that is supposed to join the coastline onto the joining node in the coastline, and combine both nodes. (Alternatively extend the admin boundary way by one segment leading up to that coastline node.)
• Do the same for the other side, where the boundary leaves the coast.
• Finally, add all bits of coastline that now form part of your admin boundary to the boundary relation if there is one. The reason you have split the coastline before is that you can now add only the relevant bits of coastline.
• Do not tag the coastline as "boundary=administrative"; being in the relation is enough. Depending on the renderer in use, this will also suppress the coastline being rendered as a boundary.

For the second boundary, do the same but of course the coastline will already be split at the right position.