Homepage Try-Dart example code issues

[chalin]

Consider making code changes shown in red to avoid the named analyzer issues:

Also, quite a few of the example files have ignore: type_annotate_public_apis which we might want to address.

Followup to #2124 (comment). cc @mit-mit

[kwalrath]

@johnpryan what do you say?

[johnpryan]

Do we need the ignore: statements or can we fix the samples?

[chalin]

We can certainly fix the examples, if you feel that the fixes proposed above are reasonable.

To give you a bit of context: All of the site's example code is analyzed under the pedantic analyzer options. Elsewhere, @legalcodes and @kwalrath gave a thumbs up agreeing that:

... pretty much all example code should be free of analyzer issues when configured with the pedantic options. -- From the short thread starting at #2128 (comment).

If you agree too, then we should update the code, including removing the ignore: type_annotate_public_apis directives and adding the necessary types.

(Btw, in case you are wondering, ignore directives in the example code don't show up in the published code because I've configured the code-excerpter to strip them out.)

[johnpryan]

That makes sense. I left some more specific comments here: #2124 (review)

[johnpryan]

I think these issues are fixed by #2124 now.