It's tough to go back searching for edits, just post a new post, that's OK.
The solder joints on the transformer aren't crap, we have received thousands of transformers from our winder and have never had a bad solder joint.
What I have seen here and there is that sometimes people get a little aggressive when they trim the wires connecting to power transformer terminals 4 and 5, and they can actually accidentally cut one of the wires leaving the transformer where it connects to the terminal. (Again, the winder cuts those wires first, removes the enamel insulation, then wraps them around the terminal and applies solder; this is not a manufacturing issue)
If you've cut one of these wires by accident, I have always found this to be a repairable issue. If you haven't cut one of these wires, but pushing on the terminals will change operation, then there's very likely a broken wire or poor solder joint that is responding to being moved by conducting properly.
-PB