FTR, OED2 has nothing to say about this pejorative usage of pear-shaped; but the online version has a New Entry marked "draft entry March 2003", which includes this:

3. colloq. (chiefly Brit., orig. R.A.F. slang). to go (also turn) pear-shaped: to go (badly)
wrong, to go awry.

1983 J. ETHELL & A. PRICE Air War South Atlantic 158 There were two bangs very close together. The whole aircraft shook and things went ‘pear-shaped’ very quickly after that. The controls ceased to work, the nose started to go down. 1989 Air Forces Monthly Feb. 53/2 When a disadvantaged fighter manages to manoeuvre back into a neutral position, it is a sign to the attacker that things are already going pear-shaped. 1995 FourFourTwo Sept. 108/1 The day itself was one of those prize-winningly crappy days when everything went pear shaped. 1999 J. CASSIDY Street Life 118 Next we travelled to Bournemouth and it was there that things began to turn rather pear-shaped.

the RAF supposition seems to be based (per usual) on the first citations found in print.