What is the difference between Server.Transfer and Response.Redirect? Why would I choose one over the other?

Server.Transfer() : client is shown as it is on the requesting page only, but the all the content is of the requested page. Data can be persist accros the pages using Context.Item collection, which is one of the best way to transfer data from one page to another keeping the page state alive.
Response.Redirect() :client know the physical location (page name and query string as well). Context.Items loses the persisitance when nevigate to destination page. In earlier versions of IIS, if we wanted to send a user to a new Web page, the only option we had was Response.Redirect. While this method does accomplish our goal, it has several important drawbacks. The biggest problem is that this method causes each page to be treated as a separate transaction. Besides making it difficult to maintain your transactional integrity, Response.Redirect introduces some additional headaches. First, it prevents good encapsulation of code. Second, you lose access to all of the properties in the Request object. Sure, there are workarounds, but they're difficult. Finally, Response.Redirect necessitates a round trip to the client, which, on high-volume sites, causes scalability problems. As you might suspect, Server.Transfer fixes all of these problems. It does this by performing the transfer on the server without requiring a roundtrip to the client.

Should validation (did the user enter a real date) occur server-side or client-side? Why?

It should occur both at client-side and Server side.By using expression validator control with the specified expression ie.. the regular expression provides the facility of only validatating the date specified is in the correct format or not. But for checking the date where it is the real data or not should be done at the server side, by getting the system date ranges and checking the date whether it is in between that range or not.

What's the difference between Page.RegisterClientScriptBlock and Page.RegisterStartupScript?

RegisterClientScriptBlock is for returning blocks of client-side script containing functions. RegisterStartupScript is for returning blocks of client-script not packaged in functions-in other words, code that's to execute when the page is loaded. The latter positions script blocks near the end of the document so elements on the page that the script interacts are loaded before the script runs. <%@ Reference Control="MyControl.ascx" %>