Well, inconsequential plot inconsistencies are one thing, but when the plots are so full of absurdity as many during the RTD era were, then it's clear the only way to enjoy it really is to just switch your brain off and look at the pretty CGI. This certainly isn't true of all stories of that time, but certainly of most of RTD's and it was a definite trend.
For me, an example of inconsequential plot inconsistencies (might have to start copying and pasting that or calling it IPI) not ruining it is The Beast Below, which is easily my favourite of the series so far and one of my favourite DW episodes. It's got plot flaws if you look closely enough, but it's interesting, funny, moving, and it's doing what DW should be doing: it's showing us new things and ideas we've not seen before (don't mention Encounter at Farpoint, it's miles better). Compared to some some backward rubbish like the RTD series finales, it's a different class.