As repeatedly said, it is considered bad practice to use the Function constructor (also see the ECMAScript Language Specification, 5^th edition, § 15.3.2.1):

new Function ([arg1[, arg2[, … argN]],] functionBody)

(where all arguments are strings containing argument names and the last (or only) string contains the function body).

To recapitulate, it is said to be slow, as explained by the Opera team:

Each time […] the Function constructor is called on a string representing source code, the script engine must start the machinery that converts the source code to executable code. This is usually expensive for performance – easily a hundred times more expensive than a simple function call, for example. (Mark ‘Tarquin’ Wilton-Jones)

Though it's not that bad, according to this post on MDC (I didn't test this myself using the current version of Firefox, though).

Crockford adds that

[t]he quoting conventions of the language make it very difficult to correctly express a function body as a string. In the string form, early error checking cannot be done. […] And it is wasteful of memory because each function requires its own independent implementation.

Another difference is that

a function defined by a Function constructor does not inherit any scope other than the global scope (which all functions inherit). (MDC)

Apart from this, you have to be attentive to avoid injection of malicious code, when you create a new Function using dynamic contents.

Lots of disadvantages and it is intelligible that ECMAScript 5 discourages the use of the Function constructor by throwing an exception when using it in strict mode (§ 13.1).

That said, T.J. Crowder says in an answer that

[t]here's almost never any need for the similar […] new Function(...), either, again except for some advanced edge cases.

So, now I am wondering: what are these “advanced edge cases”? Are there legitimate uses of the Function constructor?