Another broken 3-way Switch :/

As I've become familiar with the house wiring, I've been annoyed by the weird crap done to a house that was originally modestly, but cleanly wired. Most annoying is the fact that the house had 4 3-way switches that no longer work in very useful places. As you may know, a three way switch is a pair of light switches that can both turn on or off a light. This is VERY useful for a room that has multiple entrances. If a bedroom has a bathroom or back door connected to it, as well as an entry from a hall, you want to be able to turn on the list when entering from either door, and turn off the light when leaving through either door. Makes sense right? When people who have no business fiddling with home wiring mess with a three way, this is usually what happens:

Wouldn't it be great if the stair lights turned on and off at the switches at either end of the stairs, like they used to? 

To explain what is effectively happening: 

Another hint it's an incorrectly wired 3-way, besides the written clue and the two switches, is there is no "OFF" written on this part of the switch, because whether the light is on or off depends on the position of the other switch

If you have this problem in your house, either read my posts about three ways or leave it alone! Thank you

-Public Service Announcement from Residential Electricians

To fix means this again:

Yep it's a three way. Using your beeper lets you determine what's the hot wire and what's going to the lights. 

Lights go to the black/common pole

In these setups, the switch next to the light has the wire going to the lights that connects to the black screw while the other box has power going in and that goes to the black screw over there. The two other wires go between the boxes and the power goes through to the light when both switches are switched to the same wire. 

OK that's working. Now another one :/ 

Same situation as before in the music room also