Update:
I discovered a secret fine-tune option using the bandswitch. On my unit, even after the radio has "locked" the tuning, you can shift it up or down about 1-2 khz on the SW1 position by just slightly moving the bandswitch detent to either the left or right mechanical "bump" before actually changing bands.
The problem gets a bit worse on SW2, and you can shift it about 2-3 khz by just barely moving the bandswitch to either the left or right hand side of the bump. On SW3, this gets even worse and shifts about 3-5 khz.
I'm not going to lose sleep over it, and try to turn it into a positive little trick. Might be just enough to retune without having to go through the unlock/tune/lock routine.
I took it apart today as well. To try and reduce the bandswitch fine-tune, ahem, feature, I pulled the faceplate and tightened down the 4 screws that fit over the bandswitches themselves. They were a bit loose, so a careful tightening reduced the offset, and feels a little bit better - although my knobs have no spacer inserts so the knobs are still loose.
On the display board, I saw a Tecsun BCL-3000 V3 manufactured in 2005.
What might help the original ops problem is that the reset button might be stuck. Perhaps if one takes the radio apart and makes sure that the reset button isn't stuck down, this might help. Also seen was either the small clock/cpu battery or capacitor (I'm not sure which) right to the left of the reset button. Perhaps this has gone bad.
I also understand all the wobbliness. Not a precision bearing to be found. Just plastic sockets and slides. Although the tuning shaft which the string wraps around is metal - but the housing for the shaft is just molded plastic.
I guess that's to be expected in a $100 or less radio. Look at it this way - you get a LOT more plastic than the cheapest $100 Radio Shack scanner.
I look at it this way - if this thing lasts me 10 years, that's about $10 a year for some SWL fun before the battery, electrolytics, or something else dies.