I was always perplexed by this: due soon, or due in the next 24 hours seemed to show items due the next day, particularly if I was accessing my 'Due' perspective in the afternoon or evening. This is because 'the next 24 hours' is a moving window that progresses forwards all the time (so due in the next 24 hours at 4pm will include all items that fall due until 4pm tomorrow (or at least that's the way I think it works). The simple way I got around this, and I haven't had any problems since, is:
1. Make sure "Due Soon' is in fact set to 'In the next 24 hours'
2. In preferences, open the Data window, and set the default time for all due dates to 11.59pm.
Since I did this I find I don't get flooded with tomorrows tasks, and all tasks that appear in the Due perspective are always only todays, and I've never missed a task.
I'm open to comment and correction, but this hasn't failed me for the last 12 months.