Enable TypeScript compiler's strict mode

[andyleejordan]

Prerequisites

• I have written a descriptive issue title.
• I have searched all issues to ensure it has not already been reported.

Summary

The following options should be enabled in tsconfig.json:

"strict": true,
"noImplicitReturns": true,
"noFallthroughCasesInSwitch": true,
"noUnusedParameters": true

Proposed Design

We'll have to carefully fix all the errors and potential bugs that this reveals.

[andyleejordan]

I've made progress on this with "use strict"; in most files now!

[andyleejordan]

Getting close...