I use watercolours, artists quality. Most of the earth colours are called 'sedimenting' as opposed to 'staining'. Any reputable art shop will help you out, or Windsor and Newton do a chart showing which are non-staining. The point is that you can mix up, wipe on quickly with a soft brush and still wipe off quickly if it's not right.
A good colour for dulling down card models is 'Naples Yellow' , heavily sedimenting with good covering power which does the job beautifully, much like the plastic card chaps use an air brush with a grime colour. The most important thing to remember is only wipe once/twice with the brush and allow to dry between coats. I think acrylics are often too dense, and stain almost immediately.
Texture can be added by carefully(new blade) cutting out the very top layer of the card in small brick areas and touching up with watercolour eg burnt umber, raw sienna and indian red. Some Payne's Grey is a useful colour, but does stain, so caution! It has blue in it, so mixed thickly with the Naples yellow gives a useful 'old moss' effect I have used on the roof in the piccy above. The little bits you cut out can be stuck back somewhere else to be 'sticky-out' bits. Cut top layer of paper on the lower and side edges of some tiles/slates and tease them up a little. Just look at buildings in grimy places and copy the runs of dirt.water etc
While your at the art shop, buy a waterproof black ink 0.5mm felt tip to make 'gaps' between odd tiles and ridge tiles, and, this is a goody...draw a fine line under any protruding horizontal element that would throw a shadow at midday. or around your cut out bricks, cut out tiles etc to show where the water has got in and attracted dirt.
To make dented/bent areas, moisten with 50/50 water PVA in the appropriate area and allow plenty of time to soak in, then deform as needed, and allow to dry. The PVA stops it bending back out with consequent local changes of humidity. (Eg the dropped slate/gutter area in the lower piccy)
I then preserve my finish by spraying lightly with mat pastel fixing agent (varnish like stuff, again from an art shop)
Hope some of this helps, and that I've not been guilty of an egg sucking lesson!