A few things.
First, the mimetype from $_FILES can be easily spoofed - it take little time. You can do it using Zend_Http_Client in a few short lines of code taking little time, effort, or knowledge. This is why any reliance on $_FILES is inherently insecure - it offers exactly zero assurances.
Second, the method is public which raises an expectation that it can and will be used by end users. At present it performs its detection without any warning about the $_FILES reliance if it comes down to that. The main reason it's a worry is because, at first glance, it's an simple alternative to using the mimetype validators. This means that Debian 4.0, for example, which does not package the finfo extension or mime function is insecure out of the box if this method is relied on. You can add anything else not happy with finfo's record in PECL (prior to inclusion in 5.3 as core) or the mime function's deprecated state. Returning no mimetype is far better than returning one that's easily manipulated and can lead to holes of the bad variety.
The problem with notices is that they don't clearly demonstrate to end users that the behaviour is exceptional (only that their PHP version is somehow incomplete - wrong message!). All it will result in is broken code. Throwing an exception (it is exceptional!) with an appropriate warning message offers the benefit of allowing end users fallback themselves to an exceptional solution - you can find these anywhere running from custom magic file parsers to system commands. Developers have been dealing with $_FILES for a long time.
In a public facing method, the option to return from $_FILES is also questionable (even if opt-in). Is there a valid use case? Can't the user do their own $_FILES lookup if they need it that badly? I'm not completely against it - I simply don't see any value in it other than offering yet one more way for a developer to shoot themselves in the foot. $_FILES just cannot be trusted. If the option is needed internally - then use a protected method.
Do not commit, patch under review.