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.

6 answers

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!