Sometimes when I'm reading mysteries, I have to suspend my disbelief. That's okay, as long as it isn't too long. I want to enjoy each book I read, but sometimes that's hard to do when I'm distracted by unbelievable plot devices.
Amateur Sleuths' Involvement: Why is your sleuth involved in the case? Were they accused of perpetrating the crime themselves? Was someone close to them accused? Were they intimately involved with the victim and feel they need to track down the killer on the victim's behalf? Searching for a murderer is a dangerous activity--and the reader needs a viable reason why it's necessary for the sleuth to get involved.
Suspects' Motives: If there's only one suspect with a good motive, we'd have to assume that person is the killer. The strongest motives for killing someone are for gain (money, power), revenge, hate, love, fear (having something uncovered, losing something precious.) Usually people don't kill others for minor slights or jealousies.
Killer's Motive: I've occasionally read mysteries where I just wasn't convinced the murderer had a good reason for what they did---the story had a trumped-up feel about it. When I read those, I think, "Well, no wonder I didn't peg him as the killer. It doesn't make any sense that he'd have done it." Unless it's clear that the killer is a raging psychopath, there should be a clear reason (and a good one) that he would have risked everything to murder the victim. After all, we're talking about possibly facing a death sentence or life in prison for the crime.
Confrontation With the Killer: I covered this in a recent post (which referenced a blog post on adding suspense to your book.) Most books include a scene at the end of the book where the detective (amateur or professional) reveals and confronts the murderer. Be sure to make this scene believable. Would your sleuth really knowingly confront the killer in a deserted location with no backup?
By thinking ahead, you can make your manuscript stronger and more believable. That will keep your reader hooked until the last page.