Does Jesus' public reading of the Scriptures imply that he had any authority within the religious community? In Luke 4:17, Jesus reads from the Scriptures during a religious meeting. The passage reads, 


  Luke 4:16-21 (NIV) He went to Nazareth, where he had been brought up, and on the Sabbath day he went into the synagogue, as was his custom. He stood up to read, and the scroll of the prophet Isaiah was handed to him. Unrolling it, he found the place where it is written:
  
  “The Spirit of the Lord is on me,
      because he has anointed me
      to proclaim good news to the poor.
      He has sent me to proclaim freedom for the prisoners
      and recovery of sight for the blind,
      to set the oppressed free,
      to proclaim the year of the Lord’s favor."
  
  Then he rolled up the scroll, gave it back to the attendant and sat down. The eyes of everyone in the synagogue were fastened on him. He began by saying to them, “Today this scripture is fulfilled in your hearing.”


From a historical perspective, was it ordinary at that time for all men to read from the scrolls in public religious meetings, or does Jesus' reading imply that he had a special status within the religious community?
It would have been common for some members to recite the scriptures in same way it happens in some Churches or assemblies. Though the reciter might not be a random person but of some credibility. Jesus had a good credibility and reputation as a teacher.


  (Luke 4:14-15) 14 And Jesus returned in the power of the Spirit to
  Galilee, and a report about him went out through all the surrounding
  country. 15 And he taught in their synagogues, being glorified by all.
  
  (Matthew 13:53-54) 53 And when Jesus had finished these parables, he
  went away from there, 54 and coming to his hometown he taught them in
  their synagogue, so that they were astonished, and said, “Where did
  this man get this wisdom and these mighty works?


The reading of scripture was indeed a custom in Synagogues. A quote from The IVP New Testament Commentary Series – Jesus Preaches in Nazareth: The Time of Fulfillment Has Come (4:16-30) 


  To appreciate the account, it helps to understand the order of an
  ancient synagogue service (m. Megilla 3—4; m. Berakot 2). To have a
  synagogue service required the presence of ten adult males. At the
  service, the Shema was recited (Deut 6:4-9), followed by prayers,
  including some set prayers like the Tephillah and the Eighteen
  Benedictions (m. Berakot 2:2). After this the Scripture was read,
  beginning with a portion from the Torah (Gen—Deut) and moving next to
  a section from the Prophets. Instruction then followed. Often the
  speaker linked the texts together through appeal to other passages.
  The service then closed with a benediction.