It's possible to have a sense of midlife crisis without showing clearly defined symptoms, since it's more a state of mind than an actual illness. So a person between, very roughly 40 and 60 may have general feelings of 'not knowing what it's all for', lacking interest in their usual life, a sense of meaningless etc - these feelings are associated with midlife crisis but of course can occur at other times too.
It can be easier to think of 'symptoms' in terms of behaviour or specific problems. You may be experiencing midlife crisis if you have an affair for the first time in an otherwise happy marriage, or at least feel more tempted to do so than ever before. You may suddenly feel you can't stand your job, even if you always liked it. Some people suddenly start to drink heavily or dislike the people they live with.

You can find a full list of symptoms, with ideas for help, here.