I know people who have their dishwasher on a timer and after the meal stack the dishwasher ready to wash. I also know familes who do wash their dishes after the meal. (I am referring to observant families only.) I’m told that it is not allowed to wash up on Shabbat but I can’t stand the mess and especially in the hot summer the idea of dirty dishes soaking in now dirty water is quite nauseating. Could you please explain why it is not allowed, yet many people still do wash up?
Dishes must not be washed on Shabbat unless possibly needed to be used again on Shabbat. If you need some of the dishes you can wash the lot so you can choose which one of them to use. Therefore, washing dishes on Friday night is normally permissible; washing dishes of the last meal of Shabbat – is prohibited. If you need to wash on Shabbat for a different reason, for instance, the dirty dishes attract bugs, you may wash them, since that is for the sake of Shabbat. If a pile of dirty dishes in the middle of the kitchen will completely destroy ones' Shabbat or cause great embarrassment, one can also wash, if he can't get around the problem in any different way. You are right that some people allow themselves a lenient approach that is not according to Halacha. (I heard in the name of the Staipler Rav zt"l, that the beauty of Shabbat is a kitchen full of dishes…) For a dishwasher – there are some problems even using a timer, like the closing of the door itself creates a circuit. The different Halacha and technology institutions have solutions to get around this issue.