The sight of those photos made me wince, I was trying to be polite but that is awfull
Interference can come from the equipment plugged into the extention wiring, but more likely is the cabling itself will pick up interference. So you are trying to isolate as much wiring from the dsl signal as possible.
Having a long cable between the DSL output of the filter and the router increases the odds of that lenght of cable picking up a bit of something for the router to hear. So going for a better quality cable if you can for this link improves the odds in your favour. Which is what HPsauce
The main thing is to filter off what as much of any other wiring and equipment as possible. Looks like that has been done here.
Looking at the wiring they have the other issue is that it seems venerable to creating faults that will affect pstn and DSL regardless of filtering. Being able to visualy see the pairs is a bad sign. Its the outer most insulation thats supposed to take all the physical load of the cable.
Think of the acutual wires, only 0.5mm copper (a very soft metal). They should not be in a situation where they feel the full force of any twisting, pulling, compression. Loosing a bit of the outer insulation at one point will mean the wires will have all the physical loads concentrated at that point.
Usually when you see pictures like these you also get cabling run under carpet