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.

Explain the differences between Server-side and Client-side code?

Server side scripting means that all the script will be executed by the server and interpreted as needed. ASP doesn't have some of the functionality like sockets, uploading, etc. For these you have to make a custom components usually in VB or VC++. Client side scripting means that the script will be executed immediately in the browser such as form field validation, clock, email validation, etc. Client side scripting is usually done in VBScript or JavaScript. Download time, browser compatibility, and visible code - since JavaScript and VBScript code is included in the HTML page, then anyone can see the code by viewing the page source. Also a possible security hazards for the client computer.