1. Client must enable javascript. Yes, this is a clear disadvantage of SPA. In my case I know that I can expect my users to have JavaScript enabled. If you can't then you can't do a SPA, period. That's like trying to deploy a .NET app to a machine without the .NET Framework installed.
2. Only one entry point to the site. I solve this problem using SammyJS. 2-3 days of work to get your routing properly set up, and people will be able to create deep-link bookmarks into your app that work correctly. Your server will only need to expose one endpoint - the "give me the HTML + CSS + JS for this app" endpoint (think of it as a download/update location for a precompiled application) - and the client-side JavaScript you write will handle the actual entry into the application.
3. Security. This issue is not unique to SPAs, you have to deal with security in exactly the same way when you have an "old-school" client-server app (the HATEOAS model of using Hypertext to link between pages). It's just that the user is making the requests rather than your JavaScript, and that the results are in HTML rather than JSON or some data format. In a non-SPA app you have to secure the individual pages on the server, whereas in a SPA app you have to secure the data endpoints. (And, if you don't want your client to have access to all the code, then you have to split apart the downloadable JavaScript into separate areas as well. I simply tie that into my SammyJS-based routing system so the browser only requests things that the client knows it should have access to, based on an initial load of the user's roles, and then that becomes a non-issue.)
A major architectural advantage of a SPA (that rarely gets mentioned) in many cases is the huge reduction in the "chattiness" of your app. If you design it properly to handle most processing on the client (the whole point, after all), then the number of requests to the server (read "possibilities for 503 errors that wreck your user experience") is dramatically reduced. In fact, a SPA makes it possible to do entirely offline processing, which is huge in some situations.
Performance is certainly better with client-side rendering if you do it right, but this is not the most compelling reason to build a SPA. (Network speeds are improving, after all.) Don't make the case for SPA on this basis alone.
Flexibility in your UI design is perhaps the other major advantage that I have found. Once I defined my API (with an SDK in JavaScript), I was able to completely rewrite my front-end with zero impact on the server aside from some static resource files. Try doing that with a traditional MVC app! :) (This becomes valuable when you have live deployments and version consistency of your API to worry about.)
So, bottom line: If you need offline processing (or at least want your clients to be able to survive occasional server outages) - dramatically reducing your own hardware costs - and you can assume JavaScript & modern browsers, then you need a SPA. In other cases it's more of a tradeoff.