Sounds to me that the scan coils may be loose and mis-aligned and moving around when you tilt the tv. The scan coils are electo-magnets fitted around the tube neck. On older TV's they are secured by a jubilee clip to the tube neck. Often they have rubber wedges spacing them at the correct distance from the tube. If they move the colour and scan/tilt of the picture will be affected. On modern TV's they now tend to be permanently fixed during manufacture.
Otherwise, a possible cause (but less likely from the symptoms as you've described them):
Due to loudspeakers, large radiators or concrete wall next to the TV... if so, switch the TV off for 15 mins, move it away from the object and switch back on, does it clear?
Using a fixed magnet can permanently damage the tube shadowmask, so not advised. If the cause is residual magnetism, an engineer can degauss the TV and surrounding area with a electro-magenet designed for the purpose.
Another cause is a dislodged shadowmask, it's rare and the worst case senario as it is unrepairable integral part of the tube and would require tube replacement.
Cobweb, November 2004