Prosím vás, jak je to s počitatelností těchto elektronických zařízení. Zvláště, když o nich mluvím obecně. Myslela jsem, že pokud se použijí v jednotném čísle, tak musí mít člen a/the. Ale našla jsem ve slovníku, že mobile může být i nepočitatelný: Companies want apps for mobile and tablets that will save time.

Děkuji moc.

Companies want apps for mobile is an unusual usage and it can be explained as either 1), 2), or 3):

• 1) „mobile“ doesn't necessarily refer specifically to mobile phones; it refers (here) to any device that can be used away from a router-based wifi signal, so we understand „apps for mobile usage/coverage“, and in that sense it's an example of ellipsis [= omission of a word or words that are superfluous or able to be understood from contextual clues].
• 2) „for mobile“ can take on the same adverbial feel as similar expressions such as „for home“, „for business“ and, by extension, „for mobile (phones/devices)“, because in the context, it can't be mistaken for anything else.
• 3) „mobile“ is an adjective, and when the context is clear, the adjective alone can be enough to make the meaning understood. (So it's ellipsis again.) Here's another example:

For many, lactose intolerance can be managed by reducing dairy consumption. Others may be able to enjoy dairy after taking a lactase enzyme when they eat dairy to aid in digestion. (hilltopviewon­line).

Here, we understand (in the context) „eat dairy food/products“, but the adjective alone („dairy“) is enough for the intended meaning to be clear.

So „apps for mobile“ is unusual, but doesn't feel „wrong“ (in the context in which it's used). Usage is not always governed by grammar „rules“; semantics (= the meaning in the context in which words are used) can be just as important.