Are slips of the tongue that reveal some acts of worship, such as night prayers (Qiyam al-Layl) or memorizing the Quran, considered showing off (riya') if they occur unintentionally during a discussion, given that the questioner is keen on concealing his acts of worship and feels remorse when revealing them?

You should praise Allah for His enabling you to perform supererogatory acts and supplicate Him to increase you and keep you steadfast. You should also strive against your ego to avoid self-admiration and the desire to show off. Thinking about such things to oneself does no harm, for Allah has forgiven this Ummah for what they think to themselves. As for mentioning your acts of obedience to others, try to avoid it as much as you can. What slips out unintentionally does no harm as long as you dislike it, and it might even contain good in that listeners might follow your example. A person speaking of Allah's blessings upon him and His enabling him to obey, so that others may follow his example, is not showing off.