There is also some downright ridiculous scaremongering from both sides.
I was not impressed with either side's contribution to a BBC sports report on how How Brexit would affect English Football - in which the BBC had asked for comments from several viewpoints.
Now, I do not claim to be a great expert on football, but it appeared to me that Vote Leave did a far better job of eviscerating the case put by Will Straw on behalf of "Britain Stronger in Europe" than they did of putting their own case.
But frankly both sides were all over the place.
The football authorities are reported at the head of the article as thinking as follows:
"The FA is concerned about the influx of foreign players into the top tier of the English game, which it believes is crowding out young home-grown talent.
"Working with the Home Office, it has brought in tougher visa restrictions on players from outside the EU, to ensure only established stars can be snapped up by English clubs. The FA declined to comment on whether it would like to see similar restrictions on players from within the EU, which could only come about if Britain left."
However, Rory Miller, former director of the MBA (Football Industries) programme at Liverpool University has a viewpoint suggesting that the Premier League might want precisely the opposite to the FA, that is that they would want the right to bring in as many overseas players as possible.
Will Straw's "Remain" argument was based on the apparently unconsidered assumption that the ability to bring in lots of European players must be good for British football, citing a Guardian article which suggests that Brexit might make this harder.
The Vote Leave webpage has an article attacking Will Straw's piece which I have linked to above and which made a strong and, in my opinion persuasive, case that the assumptions behind that Guardian article were very questionable.
Unfortunately their arguments pulling the "Britain Stronger in Europe" position to pieces was about the only thing "Vote Leave" had to say which made sense - because those arguments are inconsistent with the rest of their position and damage their own case too.
Robert Oxley's "Vote Leave" piece on the BBC website does not appear to line up all that well with what the Football Association is quoted as saying, as quoted above, either. He says
"The FA has acknowledged the recent restrictions that have been introduced on skilled immigration from non-EU countries are the direct consequence of the EU's freedom of movement rules."
The argument from both Vote Leave and Leave EU, who appear to be in agreement for once, seems to be that restrictions on immigration from the rest of the world have only been imposed to counterbalance the fact that there are none for EU citizens. That is a travesty of the truth.
Those restrictions would have been necessary if the Coalition and Conservative governments were ever going to make even the most minimal attempt to honour election manifesto commitments to get net migration down to the tens of thousands, even without EU freedom of movement rules.
You do not have to be a "fortress Britain" opponent of all immigration to recognise that there are limits on the rate of net inward migration which can be accommodated without social and capacity problems and it is a simple fact that in 2010 Britain was experiencing net immigration from both EU and non-EU countries well above the rate which many people believe to be sustainable.
Returning to the specific football issues, the "Vote Leave" arguments are seriously inconsistent.
They appear to be simultaneously arguing that the ability of EU footballers to play in English leagues is a harmful EU policy which we could benefit from scrapping, and yet also arguing that the suggestion that European footballers might be prevented from playing in Britain after Brexit is untrue scaremongering by the "Remain" campaign.
Robert Oxley (and Brian Monteith of Leave.EU) attack EU freedom of movement rules in their arguments as presented on the BBC site linked to above,. They argue that the EU's freedom of movement policies have prevented British football, quote,
"from implementing policies to nurture domestic talent and from bringing the top footballing talent from right across the globe."
"This has hurt clubs' abilities to bring in players from outside of the EU while preventing any limits from being imposed within the EU. That's not a decision of anyone we elect, that's thanks to the controversial 1995 Bosman ruling in the European Court of Justice."
So does Vote Leave want to make it harder for European footballers to play here? That's the logical inference from this argument, but wait ...
In the past 72 hours Vote Leave have been tweeting that Britain Stronger in Europe have been issuing "Project Fear" propaganda about the impact on football of Brexit. They link back to the page here on the Vote Leave website which challenges Will Straw's article, accuse the suggestion that fewer European players could take part in British leagues after Brexit of being "flawed" (probably correctly) and explain that, quote,
"there would be nothing to stop the FA or Government removing the requirement for foreign footballers to obtain a sponsorship licence from the FA after the UK left the EU."
"Even in the unlikely scenario that the current rules were retained and applied to EU states, the impact is likely to be limited. Foreign players are entitled to a work visa if they are part of an association that is in the FIFA top 50. This means high quality players from Belgium, Germany, Portugal, Romania, Spain, Netherlands, Austria, Croatia, Slovakia, Italy, Czech Republic, Denmark, France, Poland, Sweden, Hungary, Greece and Slovenia would be largely unaffected."
So that is the first cognitive dissonance in the "Vote Leave" view of football.
Is the right of European footballers to play in Britain a harmful policy imposed on UK football by unelected judges, which damages opportunities for home-grown and non-EU talent? Or is the suggestion that a Britain which had left the EU might reduce the ability of European footballers to play in the UK just "scaremongering" by "Britain Stronger in Europe?" They can't have it both ways.
But there is a second cognitive dissonance in what "Vote Leave" has put out in the past 72 hours. If BSE suggestions that leaving the EU might have an impact on how many European footballers can play in Britain were "scaremongering" what do vote leave think this is?
Anyone who followed the link provided with the above "Vote Leave" tweet would be directed to a Reuters report with the title
"EU says has no plans to review British VAT exemptions."
Yes, that's right. The link provided to supposedly back up a story about the EU wanting to scrap the 0% rates of VAT in Britain actually says there are no plans to even review them.
The French EU Commissioner did express a personal view that in his opinion zero rating is not the best idea, but he also said that he has
"no immediate plans to propose ending VAT exemptions on various products in Britain"
and noted that member states would have a veto over any such proposal.
The Reuters article also quoted a British government spokeswoman as stressing there was no EU proposal to scrap zero rates and that London would veto it if there were.
"Our position on this is clear," she said. "We will keep zero rates of VAT on certain goods and services we negotiated when we joined the European Community."
So the article to which Vote Leave linked provides no substantiation whatsoever that there is any serious risk of the EU successfully forcing Britain to end zero rating on VAT.
On consecutive days "Vote Leave" was issuing tweets accusing the "Remain" side of scaremongering over football, and themselves issuing a ridiculous scaremonger over a non-existent proposal to scrap VAT zero rating, which Britain could and would veto if it ever came forward.
This kind of "project fear" nonsense is equally silly whether it comes from the "Leave" side or the "Remain" side and some people on both have been doing way too much of it. Vote Leave said we should give the "Red card to Project Fear." Yes - from supporters and opponents of EU membership.
Would it really be so much to ask for a more grown-up debate from both sides?