How to fake an "almost" Halting Oracle. For one thing, it's not a Halting Oracle, it's actually an "oracle" that tells you if you have an unspecified bug. The "oracle" doesn't answer "trivial" questions, for an unspecified definition of trivial. In reality, the "oracle" just uses heuristics to determine if the program is complex enough, that any experienced developer would tell you that there's probably a bug somewhere. The "oracle" will only answer questions about systems that are really Production systems. The "oracle" will not answer questions about systems that use Formal Methods.

If the above criteria are met, the "oracle" waits a random interval of time, flashing lights in complex patterns, then simply answers, "Yes."

seems unlikley.

if only we had some kind of improbability engine.

I doubt an improbability engine would be good for much more than party tricks. An infinite improbability drive would be much more useful, but such a thing would be virtual impossibility...

That'd be a good day.