Can selenium IDE handle any checkpoint like QTP, WinRunner.?.
Selenium is not expected to be used in the "IDE" mode. Record & Playback of Selenium IDE is just the beginning.
Export your recorded steps.
Use java/python/dotnet bindings for selenium & implement your business logic & checkpoints/assertions/error handling.
I hope this answered your question.
The verifyXXX and assertXXX are basically checkpoint. You're checking if a certain condition is True/False.
To some degree you can use some of the Eval actions to execute JS for more interesting verifications.