I can see several problems with using quotes.
1. You may not have understood the quotation properly. The original writer/speaker might have expressed themself unclearly, or you may have missed the point that they were trying to make, perhaps by reading their words too literally. Either way it is a danger.
2. The context is hugely important. Stating the blindingly obvious, the UK in 2008 is not the UK in 1945, our standard of living has changed dramatically, as has the global situation we face. Therefore it is entirely logical that a statement of political stategy that was reasonable in 1945 is unreasonable now. To remove a quote from its context may therefore make it meaningless.
3. The use of quotes, in my opinion, is usually an exercise in social proof. We quote figures who are widely respected because their reputation is a seal of trustworthiness that we add to our argument. In our narrative they are a character who can be trusted. But their words may not actually prove anything.
For example, suppose I said I have just discovered the following passage in a lost essay written by Karl Marx:
"It is possibe, if unlikely, that a capitalist system may be able to sustain economic growth to the extent that the material condition of the proletariat improves dramatically. In such a scenario the proletariat's relationship to the means of production would be unchanged, but the nature of proletarian consciousness determined by significantly changed material conditions may give rise to a pragmatic mentality that seeks incremental reform rather than revolutionary transformation. If such a condition were to occur it may not be unreasonable for the proletariat to adjust its political programme accordingly."
If this quote genuinely was from Marx it could be used as social proof that social democratic politics was a justifiable approach in a country with high living standards for working people. Unfortunately the quote isn't Marx, it's me, but does the logic of the argument lose any strength because of it? It shouldn't do should it, but it does feel like it has lost power when you know it's not a quote from anyone important. That's because social proof is another example of us using a short-cut to understand something. The writer/speaker hallmark is what we are using to judge the quote by, not the actual content.