What gets measured gets done. I would make employee input part of every manager's and employee's MBOs.
Are your managers having frequent one-on-one meetings with their employees? If so, managers should task every employee with providing their perspective on trends, risks, opportunities. I might also suggest each manager conduct a monthly or quarterly group discussion so best practices can be gained and shared to improve everyone's ability to spot trends, identify risks, etc. This is a great task to improve every employees ability to learn how to find elusvie information, think critically and creatively, and pose their recommendations in a professional manner.
The risk is that human nature may result in true risks and trends not bubbling up to management. So, in addition to the strategy above, I would also include channels that bypass the direct manager. in some cases, managers will eliminate ideas they feel threaten their perspective or approach. We've all seen management teams that spoon feed upper management and eliminate facts that may be contrary to their current approach. One idea would be to have management conduct small "focus groups" with employees outside their direct functional reporting. This allows employees to feel heard and act to surface ideas to management that might otherwise be lost in the process.