Even by his towering standards, though, the mistake he made against the Springboks in Port Elizabeth, in the third Test of the Lions 1980 series, was something special.
Playing out of position on the wing, and with the Lions clinging to a 10-6 lead they had to maintain to keep the series alive, Woodward dribbled a ball into touch, rather than hammer it into its proper place in Row Z. His mistake allowed South Africa's Gerrie Germnishuys to take a quick throw, exchange passes with Theuns Stofberg, and sprint over for a try. But it was for what happened next that the incident is best remembered.
As they gathered under the posts for Naas Botha's conversion, Bill Beaumont, the Lions captain, walked up to his fellow Englishman, put a consoling arm round his shoulders and said: "Woodward, you prat. You've just cost us the series."
The story may be apocryphal - it has also been told of an incident during an England v Wales game - but it sits well with the reputation Beaumont had for bluff plain-speaking before he tidied up his act and joined the mealy-mouthed world of rugby officialdom. But it is not the sort of yarn that will ever be applied to Matt Scott, whose reaction to Duncan Weir's costly intercept error against France last weekend suggests he might have designs on a career as an agony aunt once his playing days are over.
"I know what it's like when I make a mistake," said Scott in his best Dear Deidre voice. "I don't want everyone coming up to me and saying 'what are you doing?' and the like. I just kept reminding him 'next job, next job; it's not the end of the world'. And it wasn't, because we got back ahead and should still have won it.
"He is a very resilient character and I have been impressed with the way he has handled it. You couldn't have written a better hero-to-zero story [Weir had kicked the winning drop goal against Italy a fortnight earlier] than that, but that's just the way rugby is."
Of course, the irony of Weir's mistake last week was that it put a very large blot on the performance of a Scottish midfield that has been ticking along quite nicely just lately. Scott Johnson, the head coach, has been singing the praises of the axis of Weir, Scott and Alex Dunbar for a long time, and the jigsaw pieces unquestionably fell into place against Italy. That they fell apart so spectacularly for a few seconds against France does not suggest that the Scotland side's evolutionary process has been thrown into reverse.
The centre partnership of Scott and Dunbar first came together on Scotland's tour to South Africa last summer. However, its development was stalled when Scott suffered a hand injury during the November Test against Japan. They have now started seven games together, but it is no disrespect to any of the teams and players they have come up against thus far to say that they will have the sternest test of their young careers to date when they take on Jamie Roberts and Jonathan Davies in Cardiff tomorrow.
There could be no clearer signal that British and Irish rugby had entered a new era than when the Lions coach dropped Brian O'Driscoll for last year's third and deciding Lions Test against Australia and picked Roberts and Davies as his centres. Both players would walk into just about any side on earth and, if Wales have misfired at times this season, the blame can certainly not be laid at their doors.
"They are the benchmark for us, being the last two centres to start a Test for the Lions," said Scott. "That is probably why it will be the biggest one for us so far. Because Alex and I have had a few games together and have come to know each other we can kind of say 'right we have learned this, we have learned that, we can put in an 80-minute performance together'.
"Roberts and Davies are completely different players. Roberts is very direct, very physical: great at what he does. He will always try to beat you on the inside. He is not the guy to make an outside break; he is straight up and down.
"Davies has got a good bounce on him, a good outside break and fend as well as a good kicking game with his left foot. He has a good skill set to match. Defensively they are both solid, a great balance in that respect as a centre partnership.
"It will be a tough challenge but I always look forward to these things and it is the same with Alex. It is always good to get that chance to prove yourself against the best. I have watched those two play for years and have always admired them. It will be good to see where I am up against them."
In precise terms, where he will be is in the Millennium Stadium, an arena with a uniquely and intensely claustrophobic atmosphere he has never experienced before. In agreeing that the roof should be closed for tomorrow's game, Johnson has made it clear that Scotland are prepared to stand up in one of the most intimidating atmospheres world rugby can offer. "I have heard lots of positive things about it, its atmosphere and everything that goes along with it," said Scott.
Scott has been on an incredible journey since he broke into the Edinburgh team little more than two years ago. Back then, he was still finishing off his law degree, but he has since established himself as a fixture in the Scotland side and the player around whom Johnson wants to build his backline. And the coach has made sure Scott knows how important a player he has become.
"If he thinks you have potential to go a long way he will really hammer you and will never be off your back," said the 23-year-old. "He is like that, constantly on my back about everything. I might have had a great game in attack but if I missed a couple of clean-outs he will hammer me on that.
"He says to me 'I will keep on top of you; I will be relentless' and I am more than happy with that. If I start to rest on my laurels and think I did all right then I won't develop as a player. I need that all-round game to be a world-class centre or [with Dunbar] a world-class centre pairing. He is hard on us but it is a good thing."