What makes taking a field trip 'kosher'? The questions that need to be asked are:
What makes a movie ossur? I am not aware of any issur pertaining to the device or the concept, at least not in any mainstream halachic texts. Yes, I am aware that one can find a source for just about anything, but that doesn't make it binding or accepted (no, one's Rebba, or even a group of several Gedolim, does not count as the Sanhedrin of Klal Yiroel). And yes, one can find plenty of halachicly meaningless exaggeration, which while useful in a mussar context, has no bearing on halacha. (How often is something or someone described as apikorsus/apikorus, when the body of halacha pertaining to apikorsus clearly doesn't include it? The same goes for many lishonos such as 'ossur gomur toevah' etc, where the context and source of the statement must be taken into account.)
In other words, is a video of Rav Elyashiv Zt"l giving shiur 'ossur' or 'not kosher'?
Rather, their content and use can at times (maybe most of the time) make watching them ossur. However, two things bear consideration. As far as issurim pertaining to how one uses one's time, there is nothing unique about movies; group it with playing ball, color-war, trips, or any other form of relaxation. As far as pritzus, I will not minimize the issue, but one must consider halacha in a non-selective manner. When it comes to pritzus, there is a fundamental concept in yidishkeit and halcha of 'Ein derech acher'. This is what allows one, when some standard of 'need' is met, to go shopping, drive through Manhattan, take a subway, or take a stroll in the park with one's wife and kids. Obviously, determining "how much pritzus versus how much need" requires a daas torah knowledgeable in one's culture (Israeli versus American for example), situation, background, and needs. And yes, it would seem clear that relaxation can count as an acceptable need. (Since many will be aghast at this statement, let me ask them: ever take the subway not for a dire business related need? ever visited the zoo, at least chol hamoed? the examples I can use are endless, and I would assume you participate in some of them with the consent of your rav).
All this leads to a second question.
What does it mean ossur and mutar? I am definitely not qualified to answer this, but at least I can broach the topic. There are clearly different levels. Explicit issurim, chumrahs, divrei chasidus, things that become ossur by way of takanas chazal, to name a few. So, maybe a certain movie (let us say the animated Disney snow white, to keep things simple) has no ossur pritzus, inuendo, etc (before I get attacked: unless one has abnormal issues, the kiss in there should not bring lidei keri balayla, especially for kids; if yes, please consider Disney's bambi instead). Given a situation where it is the proper use of ones time to relax, or do an activity with ones spouse, etc, it would appear to be mutar. However, that does not make it ideal, or necessarily right, if one uses common sense (the so called 'fifth chelek of Shulchan Oruch'). Maybe it will act like a gateway drug - one movie will lead to another, especially by one's children. Maybe it will have negative influences from outside culture - less than ideal if one has another form of relaxation available that meets one's needs. As far as I know, none of these are Issurim, but definitely will have to be justified when one reaches Shamayim after 120, so common sense and of course daas Torah are needed.
In other words, there is no good hashgacha, it would be too subjective to the individual halachicly. [Apologies: Anything sharp was not directed at the questioner, rather intended to preempt certain comments that are always made when this topic is broached.]