The first example
This record has been set by Rod Laver until now.
is not actually ungrammatical -- it just describes peculiar circumstances. Suppose Laver set a new record every year throughout the history of the sport, say for example the number of tournaments won on clay in one year, surpassing his own previous performance each year, until the current year, when for the first time, no new record was set, or someone else bested Laver's previous record:
Since tennis began, Rod Laver won the most clay tournaments each year, and in fact won a greater number of clay tournaments each of those years than he had won the previous year, until this year.
The second example is simpler, since it doesn't have to be interpreted as a passive construction:
The bridge has been closed until now.
"Closed" can be an adjective describing the state of the bridge which endured from some time long ago up until the present, when the bridge was opened.
(I think this is essentially what Benjamin Harman said above in a comment.)