So, in traditional grammar these cases would be considered gerunds, not present participles, because they head noun phrases. Modern grammatical analyses of English (such as the Cambridge Grammar of the English Language) analyse gerunds and present participles as a single construct called the gerund-participle.
In any case, this error is common because some languages (I am personally familiar with Spanish, but probably there are others) have parallel constructions which are identical except for the use of the infinitive instead of the gerund.
For example the English sentence
[A new infusion [of cash] ] [allows [making the film] ].
translates as
[Una nueva inyección [de dinero] ] [permite [hacer la película] ].
The Spanish word hacer is the infinitive form of make, and, for native speakers of Spanish, this error is in fact quite common.
First of all, you are wrong. Gerunds and infinitives are not time dependent and could be used in the present, past or future.
That said, the use of gerund v. infinitive is an important topic and is often difficult to tell when to use one over the other, as it would depend on the context and intention of the writer.
Sometimes, they could be used interchangeably with little or no difference in meaning. While other times that may not be the case. I will lay down the general rules and leave it up to you to decide when to use one over the other.
1. With little or no difference in meaning
It started to rain v. It started raining. There is no difference in meaning. They both more or less mean the same thing, but if you want to get picky, the gerund form focuses on the continuation of the action while the other one focuses on the action or result of the action in general.
2. With difference in meaning
I remembered to do my homework v. I remembered doing my homework. In the first one you remembered first, then did your homework; while in the second one you did the homework first and then remembered doing it.[Again not a big difference but still an important one]
I stopped smoking v. I stopped to smoke. In the first one the action is real, it happened and you stopped doing it. While in the second one, you stopped something else to do the smoking; it hadn't happened yet.1
Now, as I said, the general rule to use one over the other will depend on the context, but gerunds are usually used for actions that are real, completed, or concrete while infinitives are used for actions that are unreal, abstract, or future.2
Best Answer
Remember that the participial form is used as a noun. Dancing on the table therefore modifies the object, us, and makes that the agent. Dance is a verb and continues from the main verb, had, so the subject is the agent. In other words, the decision to dance is made by the dancers in the first case and by the onlooker in the second.
In this sense there is no difference between have and get, because the to is understood in the first example. That's probably a result of have being used longer.
The second example doesn't use the participle because that form refers to an ongoing process. It might make sense for someone to be seeing a priest or a psychiatrist, which would happen over time, but a visit to an advisor about one question (that) would not. There's no verb you can't use here, but for semantic reasons there are some you wouldn't.