I am genuinely amazed that there are people who seem to think that there is something wrong or irritating about Roy Hodgson's speech. Some people seem to think that there is only one 'correct' or 'right' way to make the sound we signify with the letter 'r'. In fact, both across the UK and Ireland and across Europe there are several possible alternatives and variations within all of them.
One sound you can make is by closing the back of your throat and making a kind of quick but light 'growling' sound. Most French and German speakers use this but traditionally people from Northumberland and Durham did too.
Another is by 'rolling' the tongue against the roof of your mouth. Variants of that can be found in Scotland and Italy or in the French Pyrenees.
Another is by placing your front teeth on your bottom lip or by pursing your lips to make a kind of 'w' sound, though many users of this do not pronounce the 'w' in words in the same way as they pronounce the 'r'. This 'w' way of pronouncing 'r' was common amongst some Londoners. We recorded a market trader in Hackney for BBC Radio 4's 'Word of Mouth' whose speech was like that but a famous 'posh' speaker who had this feature was Roy Jenkins.
The fourth is the Received Pronunciation and 'estuary' pronunciation (like mine) where the tongue is not 'rolled' against the roof of the mouth but rather squeezed against it. However, though this is 'standard' it is by no means always the same. People from the Caribbean or the West Country or Ireland produce variants. And very significantly there is a division between those who 'sound' the 'r' in words like 'word' or 'card' and those who don't. Across the USA for example, you can hear wide variants of how marked the 'r' is in a word like 'America' itself. This depends on the position of the tongue when squeezed against the roof of the mouth and for how long or how strongly.
My view on these four main ways of sounding 'r' is that one of them is no more correct than another. All that we have done is determine that one of them belongs in the prestige dialect of educated and upper or middle class English people. We then say that it is 'correct' because, for example, that's how the queen pronounces it. This isn't logical. It's just an expression of an attitude to class, disguised as a comment about speech.
In all the silly stuff that's talked about 'lazy' speech or 'impediments' or any kind of terminology to describe some kind of failure or incorrectness in the way people speak, people never refer to the fact that RP or estuary speech does not show people sounding out the 'r' that most US, Irish, Caribbean and West Country and Lancashire and Scots people sound. Apparently a speaker like me is not 'lazy' or 'failing' or 'impeded' in my speech for not sounding out the 'r' in 'card' or 'short'.
In other words, many of the comments that people make about other people's speech are really comments about the status of one's own speech or the perceived status of what sounds educated.
Roy Hodgson is as we know a highly educated man. Listening to his speech, (not very closely) I get the impression he uses at least two, possibly three ways of sounding 'r'. And good luck to him. To my ear he is completely clear. He expresses himself easily and fluently. I can't think of any occasion I've not understood what he is saying or not 'caught' a word that he is saying.
I have no idea whatsoever whether he is a great, good, medium or crap football manager. In any of those scenarios, his pronunciation of what we signify with 'r' is neither here nor there. Making prejudiced comments about it, just makes it harder for any user of the non-standard ways of sounding out 'r' feel self-conscious and inadequate. A great deal of comments about language are of this order. Hierarchies serve the people at the top of the hierarchy.