Is there any app that notifies me when there is a flight from my location to the rest of the world under a fixed amount of money?

I very much doubt it and since I can't prove a negative just give some opinions.

i) Is there demand for such?

I very much doubt it. I think most people are not as flexible as you seem to be with location (of destination) and have restrictions in dates available for travel such that many of the results from an app of the kind you mention would not suit anyway. I take it each day notifications from the app you seek would only be for one day.

Without demand in volume there is little incentive for creation of such an app and a subscription that might make it worthwhile likely prohibitively expensive. (There would be little point in paying say $1,000 per year to be notified of and take three flights a year each with a saving of $200 relative to what you could find without such an app.)

ii) Airlines make pricing errors

It seems an app of the kind you describe would be relatively prone to find these. If a genuine error there is no guarantee the information would be useful, since an attempt to book one of those flights is quite likely to fail if the airline corrects the error between notification and booking attempt.

iii) The required database is expensive

I think subscription cost is of the order of $0.5M p.a. This may effectively rule out all but those already with access to it. (I am distinguishing between a specific app and a feature within an existing search engine.)

iv) There is a lot of data and it changes very frequently (far more often than the daily update you seek)

A daily update would be of little value to anyone notified say in the middle of the night who does not check the notification until they wake up. Availability at the very lowest prices may be very limited to begin with and seats may have sold out by then.

v) Processing burden

I think this is the main issue. You know how long a search takes just for a specific origin/destination pair on a specific date, even when restricted to a specific class of travel and even possibly to a limited selection of airlines. If established sites were to provide such a service they might not be able to respond to any of the queries they receive already - and it seems the ones they have at present are much more likely to end up with a booked flight than would the notifications you seek.

vi) Cheapskates are not attractive marketing targets

There is little point in investing in anything that pushes up the price of a product to address an audience that is solely interested in the cheapest prices.

vii) Services of a vaguely similar kind may exist

Where a demand is already satisfied there is little cause to create further supply. I imagine you could contract one of the consultancies that specialises in travel advice to 'keep an eye out' for you.

You can use Wander that allows you to search for travel destinations (rather than flights), you enter your budget and dates and you can browse destinations that fits within that budget, including flights, hotels and misc. spend (like food, etc).

Wander Travel

Not an app, but a website that does what you want: Adioso.

You can choose ranges for the starting date and duration of the trip, and generic destinations such as "anywhere", "international", "Europe", and even "somewhere warm".

For instance, try http://adioso.com/uy/montevideo-uy-to-europe-return-about-2-weeks-later