In the off season I think it is nice to keep checking for weeds especially on the warning track and spray them down, if you let weeds go you may be forever getting rid of them, I spent 5-1/2 hours tilling an infield that was not checked all winter and the weeds and their roots were very thick, the tiller just barely done the trick, weed killer killed the weeds above ground some what but not enough.
keep away from the grass when dragging, edge as necessary, warning tracks also, keep mounds and home plate areas covered to keep rain and wind from diminishing the dirt, if you have clay keep them damp and to keep them supple and easier to maintain, clay will over time become stone hard and the footing area will be very hard to work with and new replacement game clay will not properly adhere to the hard clay around the dug out areas, when you dampen and cover those areas especially in the off season check them every few days especially when it is sunny or just even hot to make sure that they are still damp and supple, the area in front of the mound can get stone hard, I like to install a short 12inch or so high snow like barrier in front of the infield outfield grass to keep any dirt from blowing up on the grass and wherever else needed, if you run the mower across or down the lips you will skim the grass down to the dirt, other than these things just keep checking and decide for your self what you can to keep your field in as close of playing condition as you see fit. hopefully me suggestions will be helpful.
Don Ervin