It is common in many cases people chit-chat while the rituals are taking place. Also, some wicked minded create obstacles to sacred acts.
What are the consequences of creating obstacles or disturbing the rituals (puja, bhajans, pravachana, japa, homa, etc.) or for constructing/maintaining temples or organising religious' events?
Creating obstacles or disturbing the rituals is to insult Divinities: For example,
यो अन्तरिक्षे तिष्ठति विष्टभितो ऽयज्वनः प्रमृणन् देवपीयून् । तस्मै नमो दशभिः शक्वरीभिः ॥11.2.23 The one who (यो ) dwells and establishes oneself firmly (तिष्ठति + विष्टभित) among the sky (अन्तरिक्षे ) destroys (प्रमृण) those who do not-sacrifice/insulting Divinities (अ-यज्वन् – देवपीयून् ) salutation and homage (नमो ) to the anger/fierce one (तस्मै ) we sign thy with ten (दशभिः ) hymns of Śākvara-Sāman (शक्वरीभिः )
Who to reach out to for forgiveness?
Oh Bhava (भव ) you are the ruler/king (राजन् ) be gracious/favorable, Pardon/spare (मृड ) towards the one hosting the Yagna (यजमानाय ) especially which donating cattle as a sacrifice (पशूनां ) especially you are the one to reach (बभूथ )
What happens if the priest/htor intentionally makes a mistake?
A priest (brahmana) who wants to spoil his own yajamāna for one reason or the other just has to alter one syllable…. Even the smallest mistake in ritual might lead to disaster: if certain mantras were said loudly, Rudra would kill the yajamāna’s cattle Caraka-Katha Aranyaka (II 128A, cf. III 229).
There are many details listed in the Garuda Purana and Manusmriti about improper antiquities towards rituals. Since this is KaliYuga most of the Vedic rituals are gone from regular usage. Mostly, the current era moved towards the principles of Yoga, Vedanta, and Bhakti methods.
Partial answer about disturbing during Purana narration:
Skanda purana: Vaishnava Khanda
- Those vile and base men who listen to the meritorious story without any faith shall meet with misery in every birth. They will never get the benefit of the merit.
- If men go elsewhere while the discourse is going on, their wives and riches will perish in the midst of their enjoyment of pleasure.
- If any man in the audience is seated on a high pedestal and is not humble, he shall be reborn as a poisonous tree. If anyone (from the audience) goes to sleep, he shall be reborn as a python in a forest.
- Even as the discourse is going on, if people make noise and disturb everyone, they will suffer the tortures of hells for a crore years (ten million years) and are reborn as rural pigs.
Skanda Purana: Brāhmottara-khaṇḍa
- Those base men who listen to the holy story without devotion, shall not derive meritorious benefits. In every birth they will be miserable.
- If men go elsewhere in the middle when the story is in progress, their wives and riches die or perish in the middle of the enjoyment of pleasures.
- Those base men who listen to the holy story with turbans on their heads are reborn as cranes. They are sinful persons.
- Those who listen to the holy story while chewing betel leaves will be compelled to swallow their own excreta by the servants of Yama in Naraka.
- The base men who talk and interrupt while the (Purāṇa) story is progressing, will be born as donkeys first and then as chameleons.
