Continuity mistake: Right in the beginning of the title sequence, Zelda and Link walk into a room and see the Triforce of Wisdom. Zelda even says it is the Triforce of Wisdom. It is green. But throughout the entire show in the episodes, the Triforce of Wisdom is shown as blue.
Plot hole: The Triforce of Wisdom is kept in Link's room up in a tower. It does seem logical to keep it with Hyrule's greatest hero to keep safe, but that's all you ever see protecting it. Hyrule is a large kingdom, and the Triforce of Wisdom is a vital part of keeping their community safe. Yet the only one protecting it is Link. And he's not with it 24/7. The room is not very secure either and is breached all the time by Ganon's forces. A kingdom like this would have knights to post all around the tower and be in Link's room when he's away. But nope, not here.
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Audio problem: In the opening title sequence towards the end, Link says "For you, Princess, anything." After he says this, he instantly opens his mouth again in a continued talking motion. But he is not saying anything. In a cartoon such as this, especially from this era, they wouldn't go through the trouble of animating just a breath after a speaking line, or even just a smile like that. It is extra animation for speaking that is not happening.