Any - and every - B-M with G10 side, 420 liners, and an AXIS lock will have some play when wiggled from the tip with the handle held at the opposite end. You have the thinner cross-section of the blade perhaps flexing, the looseness of the pivot some like for easier 'flicking' open, and the flexure of the handle, although, in fairness, the 710 has a stiffening back spacer. You have the moment arm of the entire blade length, when you grab it by the tip, to increase the torque you can apply to the pivot - and the washer spacing to contend with, too.
Now, another fly in the ointment... your lube. Too thick - and with some absorbed dust, pocket lint, or Q-Tip cotton fuzz, and you have drag that requires loosening the pivot just to work, allowing flexure. I'm betting that loosening the pivot, spritzing both sides with a decent aerosol cleaner/lube (Like a large can of RemOil from WallyWorld ~$5.) - knife held over an old rag to catch the run-off - to flush the old lube. Work the blade a bit, then close it and tighten it as required. You can wipe the rest of the knife down, too. Blue Loctite that pivot screw, if desired.
B-M QC... is fine. The greatest variation over the years has always been the tightness of that pivot screw - and the sharpness/uniformity of the blade's edge. Both are manually done - and not everyone likes the same tightness - and sometimes, the sharpener may just have been anticipating his next caffein/nicotene/sugar fix. American workers... we aren't always the best!
A little story. I got a 551 Grip and 201 Activator+ that came - out of the box - so dull, they needed heat to cut through butter. Five years later - that Grip and it's 440C met my then new Sharpmaker - as did the 201's D2. A new career to sharpen, they did finally get quite sharp. I tried a third B-M, finally, a year ago - followed by a dozen more since then - in less than a year! All came sharp. The oldest production, a 720, was from '01; the most recent production, a 760BK, from last year. Equally high standard of QC - and armhair poppers. Give B-M another chance... I am glad I did!
Stainz