The space behind the headboard is prime bed bug territory. Most headboards are hanging on the wall. If my wife is with me, we'll remove it and look behind it. This exposes a lot of possible bed bug territory. Even if you don't remove headboard, look around it. Or if you move the bed out from wall, look at the wall under the headboard.
Bed bugs could also be at the foot of the bed, but they're more likely to reside at the head of the bed. The foot of the bed, if the sheets are tucked in, doesn't allow bed bugs easy access to a sleeping host. The bugs would have to come up to the head of the bed to get you, and they typically minimize the distance to the host.
All of the stages of bed bugs are visible, at least if you don't need reading glasses and you have a sufficient amount of light. So if you're looking closely enough, you can even see bugs in the nymphal first instar stage. A fecal spot, for its part, can be as large as a bed bug itself in terms of the area it covers. The spots are basically digested blood, so most are dark in color. On a white mattress, they stand out pretty well.
Are there tactics that professional exterminators use that don't work?
No one tactic alone will be effective. A good pest control operator will develop a strategy to deal with the bed bugs that takes the particulars of the setting into account, and will return several times to check on progress. Dry ice sprays that freeze bed bugs have limited potential to reach hidden bugs. Steam has somewhat better penetrating ability. The downside of steam is that it leaves moisture behind. Dry ice doesn't leave any residue at all. Vacuuming has a role, but it has limitations, too. Some insecticides leave behind deposits that are slow to act but are effective in the long-term. Other insecticides kill on contact, but only reach insects that are in view. Insecticide resistance makes the choice of tactics more difficult.
An important thing to remember is that good professional pest controllers do get rid of bed bugs. The fine line that bed bug experts have to walk in talking to the public is the line where the anxiety and depression and so forth that can result from thinking about bed bugs too much can cause more problems than the bugs themselves would.