Motivating example (one of many):

function compare<T>(lhs: T, rhs: T): boolean {
  return lhs === rhs;
}

if(compare('1', 1)) { // Expected: Error -- I made 'compare' generic for a reason!
  /* ... */
}

Proposal

When generic type inference performs its Best Common Type operation (4.12.2), it should be an error if this returns {} when {} was not one of the input types.

This is entirely consistent with other behavior already in the compiler:

var foo = bar ? '1' : 1; // Error, no BCT between '1' and 1
function fn() { // Error, no BCT between '1' and 1
  if(foo) {
    return '1';
  } else {
    return 1;
  }
}

Open Questions

From @KamyarNazeri -- should this apply when there are zero input types? e.g.:

class List<T> {
    items: T[];
}

var x = new List(); // Probably want an error here

That seems desirable, but has some collateral damage:

function foo<T>(x: number, a?: T, b?: T) { }
foo(0); // Error, zero input types provided for inference

This would come up slightly more often than naively expected because many .d.ts authors (mistakenly) create generic types which don't actually consume their type parameters. Perhaps this warning would effectively discourage them from doing so?