Currently, not much stands in the way of rogue advertisements other than trying to be responsible and filtering your BGP announcements outbound to the your upstreams, and hoping they do the same.
The Internet routing table is so large (~290,000 routes at this very moment), that it's generally hard to build filters to lock down every single route (either: the device isn't capable of having an access list with a large number of routes, or if it happens to be, your performance would degrade so significantly due to CPU usage that you'd go back to no filtering).
While some ISPs do perform filtering on what they receive from customers (and others may require customers to register their routes in the RADB, a global routing registry), this works perfectly for you and me with say, 1 to 25 routes. In the cases of large customers (cable companies, state-run ISPs, etc.) it becomes a bit difficult to build and maintain an access list for these folks who will carry 500, 600, and sometimes even 2,000 routes, so you choose not to filter and it becomes a matter of trust and assumptions:
"You run a large enough network, so you must have done something right in the past, and we've all learned from the AS7007/SprintLink debacle, right? So please don't send me evil routes."
Long-winded and humorous history aside, this is commercial Internet in its adolescence, where people have different agendas, so without some more advancements in control plane horsepower from network equipment vendors, there's not much to do at the moment without taking the security-performance trade-off into account:
- Deal with YouTube route hijacking if and when it happens for a momentary inconvenience? Or penalize all your customers' performance to make sure keyboard cat keeps playing?