In S01E03 of Breaking Bad, why did Walt suspect Krazy 8 of hiding a shard of the broken plate? What made him suspicious, sort through the garbage, and put together all the broken pieces of the plate he'd dropped?
Walt had killed Krazy-8's cousin Emilio, and had all but killed Krazy-8 with the phosphine gas. However Walt was not at this point a ruthless killer, he had improvised the gas as a way of escaping from what was increasingly looking like a fatal situation for Jesse and himself.
He was now however faced with the job of killing Krazy-8 in cold blood, and was trying to rationalize his way out of the job, and was befriending him with sandwiches & beer in an attempt to find some means however slim of having to get out of the job of killing him. Walt is not particularly in a rush either, and Krazy-8 is not in a position to escape.
However Walt knows this is mostly procrastination, and that it is unlikely that some reasonable path out of this can be found. We've seen since that Walt is not stupid and knows that he needs a watertight reason to trust some of the people he deals with. He would only not kill Krazy-8 if he had some leverage to ensure his and his family's safety.
Walt also knows that Krazy-8 is also not stupid, and is also weighing up the chances of him walking out of the situation alive. Krazy-8 knows that it is unlikely that Walt will just let him free, as a result he will be forced to take any opportunity that arises to kill Walt and escape. They are both in a situation with a very slim chance of a negotiated 'diplomatic' ending, and they both know it.
This is the key to why Walt double checks the shard of the plate. Walt is analyzing everything happening in this situation, knowing that a bad decision or a careless move will result in his death, or worse.
Walt has been very careful with how he deals with Krazy-8 - such as to not put himself in danger. The time he passes out and breaks the plate is the only time his guard is dropped and he knows it. I think Walt is thinking through all the possible consequences of the event, and it occurs to Walt as he looks at the plate in the trash that he needs to know that he has all the major pieces.
Walt's strength is his analytical mind. I think that this is just one of many examples of Walt thinking through all the possible consequences.
I don't believe Walt suspected him of doing this at all. Remember he was going up stairs to get the key to let him go. Just by pure chance he went to throw his can away and sees the broken pieces of the plate. At that point Walt's analytical mind realized that those pieces of the plate don't add up to a whole plate. He attempts to build the "plate puzzle" and shockingly realizes his mistake in trusting this guy.
If he had suspected him of some underhanded act, he would not have went to get the key and he would not have been so upset after finding the missing plate shard.
If you think back, Jesse said something like that. He said if he were Krazy Eight he would have found something sharp and bought his time until he could make his escape and kill Walter. At the time, he was unconscious and weak, but Walter still remembered Jesse saying that. Those words came back to Walt in that instant as he opened the trash bin. He realized Domingo had the opportunity to acquire a weapon. So he checked on his hunch. And it turned out it was exactly as Jesse said it. Breaking bad tends to do that often. Something said by the characters early comes back. Like Jane saying that laying on your back can cause you to choke.
I would first and foremost agree with the other answers that it was mainly his analytical thinking and careful consideration of all possibilities that made him recheck everything including that plate, once reminded of it by the trash.
But I would also add another aspect. Walt probably also wished, if not looked, for a "valid" reason to kill Domingo. He knew deep inside that Domingo would not get out alive and that he was only postponing the inevitable. And the fact that Krazy-8 was indeed upto something sinister made this all much easier for him. I'd thus go as far as to say that deep inside Walt wished for that plate piece to be missing and this might have been part of his motivation to check the garbage in the first place.
As much as Walter was double-checking each and every possible leak in Domingo's story, he was also searching the tiniest little stain on his vest on which he could built a moral justification for a deed he had to do sooner or later anyway, in the same way like his family's security is the primary moral excuse for all of his deeds, no matter if true or not.