Lefty - - first thoughts here are in the form of questions: How well does it bolt up, does it bolt up OK with the forend off? What's the overall shape of the gun - little use/lots of use - - is there a chance the rotary has been packed with grease, etc.? What's your sense of the strength of the top lever spring? Is wiggling it possible when the barrels are closed? When you note that the top lever is slightly right of center, take your best shot at estimating how much - at 4 o'clock, at 5 o'clock, at 5:30, etc.? Normally, rotary guns like Smiths, Hunter Spls, A.H.Foxes, NID Ithacas and certain early Stevens doubles bolt up slightly to the right of center when new. The top lever, under normal conditions, should move very gradually to the left as the bolt and barrel extension wear into each other.
Remove the barrels and with a tool depress the vertical plunger that releases the top lever when the barrels are closed. Does the top lever snap smartly into its bolted position? Does the plunger itself seem to operate in an unobstructed manner?
Last, can you determine any history on the gun - - known repairs, acknowledged problems, etc.?
This info should help out here.