This entertaining, energetic crime caper has a promising, if well-worn, premise: the world's worst criminal, fearing a slide to obscurity, resolves to cement his reputation by stealing the 'Mona Lisa'. For complex reasons, the celebrated painting has been loaned to a private gallery in the UK – opening the way to cross-Channel rivalry, incompetent breaking and entering, and old-fashioned British class-based snobbery.

The humour which follows isn't the most sophisticated or original, but it's often very funny. A pair of dim policemen, called Bread and Butter, are both entertaining in themselves and an obvious target for corny puns. The opening "news segment" is amusing, highlighting just how fatuous rolling coverage can be; an inverse-Pygmalion sequence, where an upper-crust art dealer learns how to negotiate a McDonalds, is fun too. And, as so often, the most endearing characters were often the subtler ones – with wannabe hard-man Carl a quietly menacing and secretly vulnerable presence.

But there's no shortage of farcical hijinks to be found at the Edinburgh Fringe, and – although Framed! is enjoyable – it doesn't yet stand out as a beacon of its type. It's fast-paced and well-rehearsed, but it doesn't have that sense of absolutely-on-it timing which can really set the humour alight. And the production values sit in a halfway house: not quite polished enough to shout out quality, yet not rough-and-ready enough for that to count as part of the joke.

A few of the gags are bang up-to-date (the rolling news ticker, and the criminals' use of social media particularly tickled my funnybone) but others feel like they've been trotted out too many times before. In particular, a great deal of the humour relies on well-worn stereotypes – and while these are exaggerated enough to be inoffensive, I was hoping for something cleverer, something more knowing or subversive. The decision to relocate the 'Mona Lisa' to England stretches credibility, and feels particularly under-exploited; almost all of the jokes would work every bit as well if they were stealing, let's say, a portrait of the Queen.

Overall there's a lot to enjoy about Framed!, and a few harder-edged moments which hint at some social commentary hiding below the tomfoolery. But it needs more sharpness in both script and performance, and perhaps some more thought about what's genuinely comedic about its often hackneyed storyline.