22. Please check your spelling, grammar and example code for correctness before submitting an article.

picking out a couple (but obviously not all)

#7. TryParse returns a bool for whether it succeeds, not a 0 value integer... it also fails if you pass null to it, so you don't actually need to check it first.
#17. Please learn how to use the "using" keyword
#23. The two samples have entirely different behaviour... oddly enough I'm presuming the one he said was bad to do is the one that will work correctly.

Also commenting here since the original site is broken.
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What's the advantage of using a constructor like that vs a static property that basically contains the same code, this would mean you wouldn't need to create an instance of the SafeCache class to use it (however minor that is) I do think it would make the syntax of using it a little cleaner

Would also mean you could type this instead no?
DropDownList1.DataSource = SafeCache<Widgets>.Object.WidgetIds;
DropDownList1.DataBind();

That said the Activator.CreateInstance might be more of a performance hit anyway.

Have you also thought about abstracting your caching strategy out a little? basically meaning you rely on HttpContext.Current.Cache existing, if you were using this in a BusinessLogic class that you wanted to unit test I'm guessing you'd either have to go to extra effort to get it working (create a HttpContext it could use), change it to not use the cache if HttpContext.Current is null, or use some form of dependency injection to replace the httpcontext implementation with another custom one (say a static hash table)

More overhead maybe, but there has to be something said about using standard built in framework classes over rolling your own ones.