I'd say all the usage of "一下(儿)" in the examples given in the question are legit. My dictionary (Modern Chinese Dictionary came with Mac OS X) doesn't say any there is any special cases for the usage of 一下 after a verb. And my personal experience as a native speaker suggests the same.
First let me try to further explain the usage of "一下(儿)".
One can understand 下 as a standard quantifier or measure word for actions. In Chinese high school, English teachers would often teach the student the difference between instant verbs and continuous verbs. I'm not sure whether these concepts are legit in English grammar of not, but I'll borrow the two here. Normally for instant verbs such as to kiss(亲) or to kick(踢), 一下 could be easily understand as one execution or instance of the corresponding action. For other verbs such as to eat(吃) or to run(跑), it might be hard to determine the extend of the action. But when one see such action as an activity, then they can be quantified. For example eat as an activity could be from the start to the finish of a meal.
In Chinese, quantifiers are commonly used in an ambiguous manner to increase their flexibility. In the same way 一下 turned to a figurative expression of the carry out of an action or activity casually, or with mild effort or interest, for a little while, or just do something a little bit, and some times just to make the voice more informal or approachable. Basically it's express the less in some characters of the instance of the action or activity, be it time or effort or other possible aspects.
And as a native speaker, I couldn't think of any situation that is to wrong to add 一下 after a verb.
Now let's look at the two examples in the questions that are doubtful.
I will go/went to the school to play some/a little football.
Here 踢足球 is obviously the activity of playing football not the action of kicking the ball. So it could be treated as the same way as a instant verb. Thus the usage are acceptable and legit.
I return your membership card.
The usage of 一下 is also legit here but the sentence does sound awkward. The reason for that is although it is a grammatically correct sentence, it doesn't make much sense. The problem here is that it's a declarative statement without any indication of grammar aspect or tense. If you rip 一下 out of this sentence, it would become the sentence below and still feels weird.
Now, remember this is a sentence not a modified noun phrase. The intention of this sentence is hard to deduce without context. It would be something like "I return your membership card". So you can see even in English it sounds a bit weird. Normally it should be something like：
I came to return your member ship card.
So the point is that it's correct but because there isn't a common situation to use such construction in real life, it sounds weird and this has nothing to do with the usage of 一下. It's definitely a correct sentence in theory and in certain contexts.