How do you effectively convey that competitive intelligence is a team effort, requiring input from all areas of the business, particularly customer-facing teams?

Most Competitive Intel functions begin as siloed efforts within organizations. Product, Sales, Marketing, executives... they're all interested in competitors and conduct their own research for different purposes—with or without a formal CI program. But by implementing a formal CI program, the research goes deeper on the things that matter most, and wider across the company so that everyone can access it. 

But on its own, CI is just one person grasping at what they think is important for an entire organization to be aware of. It's significantly more effective when you get multiple POVs to help guide the program's efforts.

This is a great point! Competitive intelligence is definitely a team sport and should not be solely produced by Product Marketing! I always try to reinforce that Product Marketing's intelligence is only as good as what we are given. Oftentimes, sales or customer-facing teams hear about new things quicker than PMM can. So at all training interactions with those customer-facing teams I always close with a "help us help you" message asking for their help with gathering intel. If you say it consistently, they are more apt to remember! But beyond always closing with that ask in large group settings like scheduled trainings, I also always ask when I am speaking with someone 1:1, whether that be discussions with product managers (who might be doing their own research), anytime I am chatting with reps or CSMs, or even if I run into someone in the hall. Keep asking for intel and they will remember to come to you in the future!

This is an ongoing effort, and I recommend that you take the initiative rather than waiting for another team to lead this. Talk with leaders and get their buy-in and then set up recurring meetings with different stakeholders on the Sales, Customer Success and other similar teams, and come prepared with questions that spark brainstorming. Share the goals in advance so that stakeholders can come prepared with notes they might have on the different subjects and so forth. Additionally, I recommend inviting at least two stakeholders to a single meeting because it helps everyone dig deeper into their thoughts etc. 

The "effectively convey" language makes me think that sharing competitive intelligence is not part of your company's culture. That's too bad - the best way to make it clear that CI is everyone's job is for leadership to be the one setting the priority. Here are some more grassroots strategies.

1. Direct outreach to some key sellers. Not necessarily management, but the over-performers whom other sellers want to emulate. Come with some research and hypotheses and ask their opinions.
2. Direct outreach to customer success team members. They may be in a good position to ask happy customers to share what they know. After this type of effort bears fruit once, they will be less afraid to ask the next happy customer. 
3. Co-presenting sales training with these same key salespeople. Convince them to share a win--and a loss--in front of their peers. They will want to be bought into the material that product marketing is presenting.
4. Make a case to sales and marketing leadership for third-party win-loss interviews. There's nothing like real-world data to get everyone aligned on competitive intelligence.