Keep your predispositions in check. Sometimes we have pre-determined ideas about the people we deal with that may influence our ability to perform well. The old saying "You can't judge a book by its cover" rings true. Everyone deserves the same level of service and respect going in. They will only get that if you stay neutral and objective. When you arrive on scene, your attitude should never be, "Here we go again."
Take time to step away and regroup. Sometimes you have to step back and either do something else or just take a break. Many ah-ha moments occur this way. Though not very scientific, many investigators will tell you they get gut feelings and act on them. I know of several instances where a detective got an idea while doing something else, acted on it, and later broke a case wide open.
Utilize all of your resources. We sometimes overlook resources that are available to us. For example, say you need to search a wide area for a piece of missing evidence but lack the numbers to do it. In the past, we have asked our local police academy if we could use their students to help canvass the area. Don't forget to look for expertise within your own agency either. You will typically find experienced coworkers in all types of fields that may help you. Find your own expert and see if proper protocols were followed. Variances in rules, regulations, or standing operating procedures are often indicators that something was up.
Communication is a key to success. We must communicate with each other as the case evolves. I have known agencies to protect information as if it were a matter of national security. Obviously information has to be compartmentalized, but there must be cooperation in and out of the agency for an investigation to come together. Another unit may already have an answer but doesn't know the question.
Find the right person for the job. Do you have the right personnel assigned to the right task? As a manager I've learned that we have to deal with officers of various skill levels and mindsets. I have also learned that sometimes it's our fault an officer fails because we don't match up the right skill sets to the task we want accomplished. I have seen many officers shine when matched with the right opportunity.