When using a BAD lever installed on a standard lower, and after putting in my CMMG kit, I notice that sometimes (fairly easily) the bolt will lock 'back' such that there is a 1/4" (== 0.251" from calipers) gap between the bolt and the chamber insert.

Is this a large enough gap that I should be concerned about OOB discharges?  When I pull the trigger at the gap, the bolt rocks forward, but I have no spare .22 brass to check to see if it makes a firing pin indentation.

Have you shot this conversion kit before?
Does it still have gap when using the conversion kit without the BAD lever?
What type of hammer is installed in the lower, rounded or notched? Who manufactured the hammer?  The bolt may be binding on the hammer if its a notched hammer.
That is a very large gap, the hammer probably wouldn't even strike the firing pin, and you may get a slam fire possibly causing an OOB discharge.  I wouldn't shoot it till you figure out what the problem is.

I have not shot the kit, because when doing some cycling procedures I noticed this.  Whenever I use the .22 conversion, I just take the lever off (hell, even with 5.56 it doesn't function properly, the bolt doesn't lock back on an empty mag).

The gap isn't all the time, it's when the lever is tripped and actuates the bolt hold open/ping pong paddle.  I can replicate the same thing when I remove the BAD lever, it's just much much harder to do (and takes quite a bit of intentional force to do, i.e. forcing the ping pong paddle down).  

The hammer is a standard DPMS hammer from an LPK (so... rounded?).

With regard to trying to figure the BAD lever out, I think I might just get a dedicated .22 lower and then wait for the bolt hold open posted in the sticky.  Then it will likely all be kosher.

Well you definitely don't want to try firing the gun with the bolt 1/4" OOB.  Most likely it wouldn't ignite the primer, but if it did, you'd have case fragments going everywhere.

Sucks that your BAD doesn't work right. Mine work like a charm on both of my guns, now that I have used it I could never go back.

I would send the BAD lever back to Magpul for replacement.