Is it all right to use the two verb tenses in the following sentence when writing a cover letter?

I developed communication skills as an Assistant at Oakly Inc., catering to the needs of my supervisor and assisting at the front desk.

Yes. That construction is fine.

Thanks for the answer Ms. Sue, do you have a resource you could share as to why that is?

Read about participles here:

http://grammar.ccc.commnet.edu/grammar/verbs.htm#participle

~ Use of the present participle (-ing forms) is consistent with the tense of the main verb.

~ Use of a past participle (-ed and other past participle forms) indicates something that happened BEFORE the tense of the main verb.

http://www.towson.edu/ows/tenseconsistency.htm

I'll take your answer to mean that you agree with Ms. Sue in that the construction of the sentence is okay, Writeacher.

Yes. Both of us were referring you to tense consistency.

Keep in mind that, in your sentence, the main verb is in the simple past -- "developed" -- and the two participles (not main verbs) are present participles -- "catering" and "assisting." Thus the actions of the verbs develop, cater, and assist were pretty much simultaneous.

Switching main verbs from one tense to another in a paragraph or an essay, however, is a big no-no! You'll confuse the heck out of your readers!

Yes, it is generally acceptable to use two verb tenses in a sentence, as long as the intended meaning is clear and there is no confusion. In the sentence you provided, the verb "developed" is in the past tense, while "catering" and "assisting" are in the present participle form, which is often used to indicate ongoing or continuous actions.

If you want to maintain consistency in verb tenses, you can use the past tense for both actions mentioned in the sentence. For example, you could revise the sentence as:

"I developed communication skills as an Assistant at Oakly Inc., where I catered to the needs of my supervisor and assisted at the front desk."

Alternatively, if you want to emphasize that the actions of catering and assisting were ongoing or continuous, you can keep the present participle form. In this case, you could revise the sentence as:

"I developed communication skills as an Assistant at Oakly Inc., catering to the needs of my supervisor and assisting at the front desk."

Ultimately, the choice between using consistent verb tenses or a combination of tenses is a matter of style and personal preference. It's important to ensure that your intended meaning is clear and that the sentence flows smoothly.