When a car is washed (usually infrequently), many people use the minimum possible amount of water, and some start by scrubbing thick mud from the lower parts of the vehicle. This results in the sponge or cloth becoming impregnated with grit, which can then be spread around the rest of the vehicle, including the glass.
While there is no need to use a hose (and the large quantities of water that entails), it is worth applying plenty of water from a bucket, and in the first instance ensuring that the water soaks into the mud, without rubbing hard. This will help to loosen the dirt, but minimise damage to the paintwork.
It’s best to use a purpose-designed proprietary car wash shampoo product, which will help to ‘float’ off stubborn deposits of dirt. NEVER use washing-up liquid as it contains salt, which is harmful to the vehicle.
Initially use a soft sponge and a large bucket of warm water, and always start at the top of the vehicle.
This method dates back over 100 years. My grandfather used to tell me that this approach was always adopted in the early years of motoring, before the roads were surfaced with tarmac. The mud from the unmade tracks of the time used to cover the lower parts of the vehicles of that era, so the cars were always washed from the top downwards (so that the water from the upper, cleaner parts of the vehicle would run down over, and soften, the mud deposits lower down). Although these days most roads have tarmac surfaces, they can still become very muddy, so the approach is still worth following, for best results.
A second bucketful of clean warm water, and a fresh sponge, can be used for rinsing off the remnants of the dirt and shampoo suds, then follow up with a third bucketful of warm water, plus a ‘squeegee’ device/wiping blade , then a chamois leather (real or synthetic), for wiping off/mopping up remaining water droplets, to leave clean, shiny surfaces.
For harmlessly removing stubborn deposits from the paintwork, and from around the window seals, the gentle application of an old, soft-bristled brush is effective.
In the long run this approach will minimise the chances of scratching the vehicle’s glass and paintwork.