The PLAs are still relatively new (Google shifted from the old free product ad system to PLAs last summer), so not everything about their ranking algorithm is yet fully understood. However - it is known that both CPC and product feed relevancy are definitely contributing factors.
There are only 6 ad spots for Product Listing Ads. The good news is that if Google thinks you have more than one product that should show up in PLA for a search - they will sometimes put your ads in more than one spot along with competitors. This is something you don't see with text ads, where only one advertiser can show up on a page at any time.
That being said - the best way to try to 'rank' your PLA ads better is to optimize your merchant center data feed. Give Google as much detail as possible in your feed. Be as descriptive as possible with titles, product descriptions, and also be sure to set the most appropriate category or 'product type' as they call it.
Google gives you 70 characters for the title. Use them well, with the best keywords suitable for that product (without looking spammy). Descriptive, relevant, and to the point.
Make sure descriptions are clean and free of odd characters and unnecessary numbering, part numbers, things like "
call us to ask about our specials" etc. Basically anything that you as a customer wouldn't care to see in an ad. Think of descriptions and titles as a way for you to personally tell someone at Google what that particular product is and what it is for.
If you have a large datafeed, this can be done with a script or Excel macros. Otherwise, a VA or someone can go through it and clean them for you. Again, include keywords you want in there that would match with what you are trying to get your Adwords campaign to achieve.
Also, make sure your uploaded feed contains no warnings or errors after submitting. You can check this by going to the 'Data Quality' screen in Merchant Center.
You don't want to be seeing things like this:
Note that some recommendations are not errors. That means that they will accept those submissions - but those problems can hurt your ranking.
Set up scheduled feed updates and make occasional tweaks and changes to your titles, descriptions, or images to keep things fresh. Although there is no proof to support this - it is likely that Google will favor (rank) merchants more who are keeping things up to date vs. stagnant ads that remain unchanged for months. (It's known that Google prefers frequently updated sites over stagnant ones when they rank websites, so there's no reason to believe they wouldn't do the same with product listings).
When setting up your product targeting in Adwords - do NOT attempt to target 'All products' in more than one campaign. This will actually result in conflicting targeting, and according to Google - may result in none of your PLAs showing up at all, or not very often. Instead, target only those product id's that are relevant to that campaign or adgroup and keep them out of others.
I'm not sure what you mean here exactly. Care to share a screenshot?