I recently fixed tuning problems on three TV's in very different situations. All the problems came down to poor connection on the aerial lead from the wall socket to the first input. One cable was ancient, one was new and one very expensive but they were all problematic. I replaced them all with cheap alloy uhf plugs made by Ross and bought from Rober Dyas for about £2.70 a pack of two. They do not need soldering because there is a screw clamp on the central conductor.
Simples!