Eager Loading and shaping the result: EF4 eager loading system (Include("Path")) generates improper SQL, with looping JOIN's , which will execute thousands(not literally) time slower for many-to-many relationships then hand written SQL (it's effectively unusable).
Materializer can't materialize associated entities: If you can think you can overcome previous problem by providing you own SQL query, you are wrong. EF4 can't materialize(map) associated entities from JOIN SQL query, it can only load data from one table (So if you have Order.Product, SELECT * FROM order LEFT JOIN Product will initialize only Order object, Product will remain null, thought all necessary data is fetched in query to init it ). This can be overcome by using EFExtensions community add-on, but the code you will have to write for this is really ugly (I tried).
Self-Tracking Entities: Many say that Self-tracking entities are cool for N-tier development including the top answer in this thread. Thought I haven't even give them a try, I can say they are not.Every input can be forged, you can't simply take the changes that user sends you and apply them to data base, why not give the user direct data base access then? Any way you will have to load the data user is about to change from DB, check that it exist
not exists do permissions checks etc etc. You can't trust user on the state of entity he is sending to server, you will anyway have to load this entity from DB and determine it's state and other things, so this information is useless, as do Self-Tracking entities unless you do a private trusted n-tier system for internal use, in which case maybe you could give just plain DB access. (Thats my thoughts about ST Entities and N-tire, I'm not very expericned in N-Tier, so it can change, if I misunderstood something here comment it)
Logging, Events, integrating business logic: EF4 is like black box, it do something and you have no idea what it do. There is only one event OnSavingChanges where you can put some business logic you need to run before something happens with DB, and if you need to apply some changes to business objects before something happens you will have to dig in ObjectStateManager, and this is really ugly, code can become huge. If you for example using Repository pattern and what to be notified on changes made to DB in clean object way, you will have hard time doing this with EF.
Extensibility: All EF code is private and internal, if you don't like something (and you will not like a LOT if you are serious about EF using), no way you will change this in easy way, In fact I'm sure it's easer to write you own ORM from scratch (I did) then make EF work as you need. As example take a look at EFExtensions source, it's based on extensions methods, and different "hacks" to make EF little more usable, and the code is pretty ugly (and it's not authors fault, when everything in EF is private this is the only way to extend it).