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I would like to know, in the following case, which one is correct:

"This condition plus some other properties ensures that..."

or should I say:

"This condition plus some other properties ensure that..."

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As you probably know, if the word plus were replaced with the coordinating conjunction and, then the subject would be plural and it would take a plural verb:

The dog and the cat were hungry.

The question is thus about whether to treat plus as a coordinating conjunction. It's actually a special type of coordinating conjunction--a copulative conjunction.

From Grammarist:

The six words most commonly used as coordinating conjunctions can be remembered with the mnemonic device FANBOYS—for, and, nor, but, or, yet, so. (Source)

...

Copulative conjunctions (also known as additive conjunctions) are coordinating conjunctions used to denote addition. The conjunction indicates that the second word, phrase, clause, or sentence contains an additional fact that is related to the earlier word, phrase, clause, or sentence. Some of the most common copulative conjunctions are and, also, as well as, moreover, no less, and plus. (Source)

So, while plus is not one of the typical seven coordinating conjunctions that you generally hear about in grammar texts, it can be considered a type of coordinating conjunction and the same rules about plurality apply.

So the correct answer is:

"This condition plus some other properties ensure that..."

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