Most collectors who have a 17th century Salzburg thaler will have an image of Saint Rupert (Ruprecht) on it. Rupert is generally credited with reviving the abandoned Roman town of Juvavum, and renaming it Salzburg. He (sometimes shown with his successor Vergilius) is patron saint of the city and region. His remains are in the Salzburg cathedral.
So, this 1682 half thaler (there is also a 1682 thaler with similar reverse) has a different design, with a "team" of saints reverse. The interior legend obverse states the purpose of the coin:
VNDECIMO SAECVLO | FVNDATI ARCHIEPTVS SAL |ISB:
Translation: 1100 (YEAR ANNIVERSARY) CONSECRATION OF THE ARCHBISHOPRIC OF SALZBURG
The reverse legend in the exergue reads:
SS:MARTIN'EP:VINCENTI'm:HERMES M:CHRYSANTH'ET DARIA MM:TRANSLATI
Translation: SAINTS MARTIN BISHOP, VINCENT MARTYR, HERMES MARTYR, CHRYSANTHUS AND DARIA MARTYRS, TRANSLATED
First the coin (just won at auction), and then some explanations!

Modern historians place the date for the revival of the bishopric of Salzburg under Rupert (born 660, died around 710) at about 700 A.D., so this 1100 year commemoration in 1682 turns out (in hindsight) to have been premature by about a century.
As for all those saints on the reverse ...
In medieval times, pilgrimage was an economic engine similar to tourism. It was great that Salzburg had its two local saints interred in the cathedral, but this meant little to the devout outside the region who had never heard of Rupert. To attract pilgrims from afar, you needed star power: relics of an apostle, an early martyr, or some other saint(s) renowned through the Christian world. No matter that such a saint hadn't lived or (even better) died in your part of Europe, because there was another option.
Translation.
This was the name for the process in which relics were brought from one place to another, often with great ceremony (and rarely with much attention to authenticity).
So this is also what the reverse of this coin is commemorating: the translation (TRANSLATI) of relics of these non-native saints to Salzburg. In order:
1. St. Martin (died 397 A.D.) is a known historical figure, a former Roman soldier who resigned his first profession and became the bishop of Tours (France). He is shown with his mitre and staff. His relics are believed to have been brought to Salzburg in the 9th century
2. St. Vincent was a deacon in Saragossa (Zaragoza) Spain who was known to have died in Valencia during the persecutions of Diocletian in 304 A.D. He is the patron saint of Portugal, and of Berne Switzerland (go figure?), and some of his relics were brought to Salzburg around 900 A.D.
3. St. Hermes was purportedly a Greek who was martyred in ROme in 120 A.D., but about whom little else is known. A relic was brought from Rome to Salzburg in 851.
4. Chrysanthus was purportedly the son of an Egyptian patrician who became a Christian, moved to Rome, married Daria a Roman woman, and both were executed around 283 for converting Roman citizens to Christianity. Some of their relics were gifted to the Archbishop of Salizburg by Pope Nicolas in 860.