Hugh Grant's Jeremy Thorpe has his hair parted on the wrong side - the right side. The real Jeremy Thorpe always had his hair parted on the left side. (See Google Images.)
When Holmes is at home in 1975 and the telephone rings they are watching the Fawlty Towers episode 'Basil The Rat'. This was actually part of the second series of Fawlty Towers and was not broadcast until 25 October 1979.
Many of the cars shown are of the wrong age - for example the Commer van in which Scott's first wife left him being at registered at least 2 years after the event depicted. The same applies to the Hillman Hunter shown after the death of Thorpe's wife.
Hugh Grant is approximately 20 years too old to portray Jeremy Thorpe and although Thorpe was not a young looking man, this is immediately obvious.