There are inconsistencies in how building certain improvements does or doesn't remove terrain features (Forests, Jungles, etc.) on that tile. Often, early versions of certain improvements do not remove forests therefore it's preferable to build an early version of the improvement and upgrade it through being worked by nearby city. This requires disabling of hiding obsolete worker improvements in BUG menu and even with the option disabled later workers are usually unable to build the old improvements. I've tested which improvements remove which features and the results are in the attached file (sheet Feature compatibility).
There are inconsistencies in whether or not certain improvements are buildable on certain combinations of terrain types, features, etc. I've thoroughly tested this as well and the results for Workshop, Cottage and Farm are also in the attached file (on their respective sheets). Other improvements seemed fine, or the inconsistencies were minor and are mentioned later in this post.
Not sure if the Tree Nursery improvement, after growing into Young Forest and later into Plant Forest, should also place a forest feature on the tile as does the late game Plant Forest worker action (available when terraforming/reforestation option is enabled), but it doesn't.
On Permafrost, it's possible to build Tree Nurseries, but it's impossible to plant any features.
Cacti terrain features cannot be removed at all, only by planting another feature over it.
Windtrap improvement seems like a late game version of the Windmill improvement, but cannot be build on Mountains even though Windmill can.
It's possible to build Lumberjack and "Gather Wood" (the first tier of the improvement) on Jungles, but it's impossible to build Lumbermills.
Jungle tile feature seem to block building of many different types of improvements on certain terrain types (see the attached file for more details), it also appears that you cannot build the Ancient Relics special improvement on Jungle tile. This is quite strange since it can be removed by chopping it down and the improvements can be build there afterwards. Similarly for Swamps and Peat Bogs.
Rapa-Nui Workers' pedia description states that they should be able to build special Moai improvement, but they cannot. No such improvement seem to exist either.
Different worker units are supposed to have different work rates (and they appear to), but these work rates don't seem to be displayed anywhere. This means it's impossible to tell how much of a work speed upgrade are you getting when upgrading workers without extensive testing.