Q:

Choice of aspect for infinitives

I'm pretty comfortable with the use of aspects in conjugated verbs. However, the choice of aspect for infinitives still gives me trouble. I recently read the following snippet, in which twice the act of paying fines is referred to in the exact context both times, however one is perfective and one is imperfective. Assuming this is correctly written, what is the logic behind the choice of aspect in each case?

Мы выехали рано утром и через несколько часов обнаружили что водитель
  забыл его водительское удостоверение. В поездке он вынужден был
  заплатить два штрафа. В конце нашего пути мы поняли, что пересекли
  пограничную зону и каждый из нас вынужден был платить штраф.

A:

Leaving aside the ugliness of this excerpt, the choice of perfective/imperfective is sometimes absolutely free.
On the first occurence, the speaker says about what already happened, while they were riding. Thus he/she must use perfective.
But on the second occurence he/she has a free choice. The difference is really subtle. By choosing perfective one shows again that it's all finished already. Yet by choosing imperfective one gives a slight feeling of "presence".
Putting it into other words, if you would have translated the first sentence into English, you couldn't use the continouos tense (you may be paying twice, but not paying two fines in different places/times etc.). Thus you couldn't use imperfective here. But in the second sentence there's no such restriction. I know, everyone would go with simple tense here too, but technically you might choose free. In Russian there's no such thing as "indefinite" tense, so you have to choose one of two.
Your problem probably lies in the observation that the speaker uses different verb types in the consequent sentences. But it's not the fault on itself. They belong to different setups, so one may mix them, just like English speaker mixes perfect/continouos/simple tenses.

A:

Мы выехали рано утром и через несколько часов обнаружили что водитель забыл его водительское удостоверение. В поездке он вынужден был заплатить два штрафа. В конце нашего пути мы поняли, что пересекли пограничную зону и каждый из нас вынужден был платить штраф.

I am afraid it's a bad translation from English. Your second sentence should sound as 

каждый из нас вынужден будет платить/заплатить 

The first sentence refers to a completed action so a perfective infinitive should be used.It means "He had to pay and he did it.
The second sentence refers to an expected obligation where the choice of the form платить/заплатить doesn't influence the general meaning 

