At a casual look, grass with a bit of surface water on it can look very similar to a potentially deadly marsh, and in many rural places there can be lots of both after it's been raining! In dry weather it's easier to spot, since most wet ground will be somewhat marshy.
When it's been raining though, is there a good way to tell the difference other than to put your foot in and see?
You can get a lot of the way towards understanding which ground has a good likelihood of being marshy from full use of Ordnance Survey (or equivalent) maps, and looking at the type of rock in the area you will be hiking.
Good quality maps give a lot of detail around topography, so you can look at slopes and heights near watercourses etc. If you are on a flood plain you have a reasonably high likelihood of marsh, whereas a steep slope will not be.
Being aware of the type of rock around you will help a lot - limestone country will probably not give you marshland, but poses a higher risk of sinkholes etc as it is very porous and easily eroded.
Looking at the type of plants growing around you will help - bullrushes, reeds etc. are an indicator of waterlogged ground.
Some maps even mark marshy ground - which helps:-)
Some additions to the answer above:
