Pieter, I doubt many will be plotting by lineweight as you probably can tell by the previous threads on the matter, but to answer your questions ....
How are you achieveing screening?
We have not had the need for screening, not that it would not come up in the future, we have just never had the need for it.
Do you use the default monochrome colortable?
Yes
Are you running into any problems?
Only when someone sends a drawing specifying a plot by color scheme and we have to setup the lineweights.
The linework for your blocks are you setting weight's by-layer or by-entity?
In short bylayer .... but ...
We have adopted a little bit different approach with blocks. While in most standards, you see blocks all created on layer 0, then inserted on the correct layer, it sometimes can create a problem, especially if the block was defined with lineweight as bylayer. So ....
We defined ALL entities within blocks on their respective layers. Now when we insert a block, the layer lineweight can apply to the layer itelf, rather than the block. We have not had any serious problems with this scenario to date.
Are you controlling the weight by-layer or are your entities on their own?
Default ByLayer .... occasionally the need arises to assign an entity lineweight, but those are minimal.