Hello, I wrote an answer about the usefulness and reliability of the Tapestry to a modern audience here.

As to a contemporary one; the earliest years of the Tapestry are somewhat shrouded in mystery. There's still a substantial debate over who had the tapestry produced, where, and precisely why, although the general consensus is that it was created on the orders of William I's brother, Bishop Odo, Earl of Kent. The textile and the embroidery pattern suggests that it was produced in Kent, probably in Canterbury. Whether or not the Tapestry was ever actually displayed, we can't say for sure, although Dodwell (1982) and Clarke (2013) support the hypothesis that it was commissioned by Odo in the immediate wake of the Conquest as he consolidated his new position as Earl of Kent, and possibly displayed in Canterbury, but was mostly intended for the dedication of the new Bayeux cathedral - also commissioned by Odo - to be displayed at the Cathedral's dedication, and then remain there as a testament to Odo's wealth, power and position.

The Tapestry - which is actually an embroidery - is ideally suited to public display. Opus Anglicanum was well-known across Europe at the time as high-quality, luxury needlework, and although the Bayeux Tapestry is in a less ornate style, the intricacy and detail would still be recognisable as a status object. It's likely that the Tapestry would be displayed around the Cathedral precinct, or indeed inside the Cathedral itself, likely in a similar way to today. The clear visual narrative and easily identified characters help to display the narrative of the 1066 conquest effectively to an audience with likely limited literacy, while the multiple appearances of Odo and his lieutenants emphasises their importance and rewards their loyalty.