Yes, I believe the "church" was given authority by Jesus, but the question should be to whom was meant by the church and how long was this authority to remain with them?
In the first century, there were apostles who along with designated disciples started local churches. They ensured that there were leaders who were grounded in the faith. We see that even from the first, there were challenges to the orthodox faith. I believe the Holy Scriptures - the Bible - was given as the authority and from when it was first being written, it gradually substituted for the apostolic authority once the individual apostles died
But that does not pan out in reality. In reality, :
1. while the majority of what we now consider constitutes scripture, there were other texts (valid or not--the 'not' being Gnostic ones in particular) which were held in esteem
2. Even valid scripture was not completely accepted or available everywhere -- between AD 50 to 150 a number of documents began to circulate among the churches. According to Jerome, this included the Gospel of the Hebrews (the Gospel of Matthew that is attested as far away as the Syriac Churches in India). You also had epistles, gospels, acts, apocalypses, homilies, and collections of teachings circulating. While some of these documents were apostolic in origin, others drew upon the tradition they had utilized in their individual missions or were summaries of the teachings.
3. By the end of the 1st century, some letters of Paul were collected and circulated, and were known to Clement of Rome, but still the idea of scripture is the Tanakh. He may refer to "words of Christ" and to epistles, but there is no compendium noted.
4. Even later, Irenaeus in the 1st century cites 21 books excluding Philemon, Hebrews, James, 2 Peter, 3 John and Jude
The net effect is that apostolic authority still was utterly necessary until (and necessary after) the Council of Nicea for ensuring that one stayed true to the faith.
I think it was Ignatius or Irenaeus who said that if anyone comes to you with the good news, ask him where he learnt it and where the person he learnt from learnt it and so on to trace back to the Apostles. Only then should you be satisfied with it -- this is nothing but apostolic authority.
****Now very importantly, books were not widely available until the 16th century and still cost a lot even then. The majority of the population including nobility were illiterate because, well, it didn't make sense to waste time learning to read and write when books were not easily available and cost more than a year's earnings for a labourer. Hence apostolic authority was necessary to still ensure that you knew who was telling you things was telling you correctly and wasn't an Arian or Gnostic