Each form submit will be processed separately, possibly many in parallel. Depending on your application this may or may not screw up data server-side. The server-side script may stop processing if the HTTP connection is dropped though (upon clicking "Submit" again, the first request is canceled and a new request send).
To avoid problems with multiple submissions, you can for example send a unique ID with the form that will be checked on the server and can only be used once. Or you can set an "already-processing" flag in the user's session. Or you can work with job-queues and check if a job for the user already exists. The specifics would depend on your application.
Re: "Any problems at the client end? for example when webserver send two responses?"
Whenever your browser sends a request, it establishes a connection to the server on which it will wait for a response. New request, new connection. When you click a submit button a second time, the first connection is dropped and a new one established (that's also the point where the server usually stops processing the old request). That's why you can load multiple pages of the same site in a browser at the same time, it won't get confused which response is meant to go into which tab.