Lee Briers kicked 5 drop goals in a Super League game against Halifax in the early 2000's. I believe he holds the record still. Warrington still lost that day if I remember right.

The RFL web-site lists 5 as the most drop goals in a match by one player...

[listDanny Wilson (Swinton) v Hunslet (John Player Special Trophy) - 6 November 1983
Peter Wood (Runcorn Highfield) v Batley (League) - 21 October 1984
Paul Bishop (Warrington) at Wigan (Premiership Trophy semi-final) - 11 May 1986
Lee Briers (Warrington Wolves) at Halifax Blue Sox (Super League) - 25 May 2002
[/list:u
I was at the last one.

Only 4 drop goals from 1 player (Johnnie Blair), but 5 in the game for Fax when they beat Wakefield 7-3 in the 1980 Challenge Cup Quarter Final. There were 6 drop goals in total in the game, with 1 each for Jimmy Birts and David Topliss as well. In those days, we could muster nearly 13k fans between us to come and watch.

Australian record is held by Souths fullback Eric Simms who kicked 5 against Penrith in 1969 when they were each worth 2 points. His drop kick abitity led to a call for a game change to reduce field goals to 1 point and this occurred soon after. Simms kicked a record 29 in a single season and over 80 in his career.

Missed drop goals is an interesting one, there was a fair few in the 2002 Grand Final by Deacon, Long and possibly Sculthorpe? I seem to recall Deacon having a go from around 50m out!

They are dropped goals.