When I try to adjust a pad to be leak proof, and eventually give up and replace it it is common for it to have one of the following.
1. A single small blob of glue somewhere, and the rest of the back of the pad 'floating'.
2. Contact cement instead of a hot-melt glue, with the contact cement only attaching the pad by the very edge of the back, while the rest of the pad 'floats' freely in a key cup with a dished back.
3. There is a thick sector of cardboard dilling part of the key cup. attachment is insecure, so that the pad can sea-saw a little on the edge of the cardboard.
5. A hot melt glue that has the consistency of cheese, and adhesive properties not much better.
6. A pad of highly inconsistent thickness.
If you buy a cheap sax, AND it has problems with getting pads to seal reliably, then there is a very good chance that one of the above is lurking in the key cups.
Key cups that are not concentric with tone holes easily present a reliability problem, because they tend to fail to seal where the pad is slightly thinner near the resonator or where there is less support near the edge of the pad.
Another common problem, in my experience more with student Yamahas than with most Chinese saxes, is that there is a lot of play in the pivot tubers of the stack keys, especially the right hand ones. Also, there is excessive play between the stack key hinge rods and the holes in the posts that they go through. This interferes with reliability of linkages. It is fortunate that Yamahas are so well designed acoustically that they still respond well even when they have small leaks.
Some saxes, especially Chinese, have the sloppiness in pivot tubes filled with high viscosity grease, so that the play is not immediately apparent. Once a load is put on the key for a while during playing, or put on in a different direction when the sax is at rest and under spring tension, the grease probably gradually moves inside the pivot, effectively moving the pivot tube relative to the rod inside, and messing up adjustments, especially linkages.
When the adjusting screws on the arm form F# to Bb and G# have 'squishy' natural cork on their tips, the typically small, edge-of -the-cork area of contact with the G# key and Bb key gets quickly crushed, messing up adjustments, Then when the screw is turned for re-adjustment, it presents a fresh 'edge' of the cork, which then proceeds to be crushed.... etc. Some saxes have very soft squishy rubber here, which can never offer a reliable transfer of force. I have found dome-shaped, high quality composite cork to be most stable here.