Learn Spanish (Latin America): ¿Nunca has visto un espejo intacto aquí? - Have you never seen an intact mirror here?

Visto is the irregular past participle of ver (to see). While most Spanish verbs form this piece of the present perfect by adding -ado or -ido, ver is one of the common exceptions you just have to memorize, similar to hecho (done/made) or escrito (written).

Why isn't there a no in this sentence, like "No has visto..."?

In Spanish, if a negative word like nunca (never) comes before the verb, you drop the no. If you put nunca after the verb, you must include no before the verb. So, you could also phrase this as: ¿No has visto nunca un espejo intacto aquí? Both structures are very common and mean exactly the same thing.

Could I use the simple past here and say "¿Nunca viste...?"

Yes, absolutely. In many parts of Latin America, native speakers actually prefer using the simple past (viste) instead of the present perfect (has visto) when talking about life experiences. While has visto translates neatly to "have you seen," you will very often hear ¿Nunca viste...? (Did you never see...?) in everyday Latin American conversation.