It's actually rather clever, calling this The Android Invasion. By announcing the main concern prominently in the title, the viewer is distracted from realizing that the invasion hasn't actually happened yet. So when the Doctor and Sarah arrive on Earth and find masked figures shooting at them and UNIT soldiers walking jerkily over cliffs, we already know that the problem has something to do with androids, and we (sort of) assume that all the other anomalies (the brand-new money, the deserted village) are related.
This does come at a price though; because we already know that there are android problems in the town of Devesham, there is a bit of a sense of "get on with it" as we wait for the Doctor and Sarah to catch up. Director Barry Letts doesn't help with this either, as he has a number of relaxed moments (such as watching all the villagers get off that truck and slowly take their places in the pub and wait for the clock to chime) that add to this almost casual feeling. Even the cliffhanger to part one, as an alien secretly observes Sarah rescuing the Doctor from a cell inside the Space Defence Centre, feels oddly loose and not the shocking/impressive moment it should be.
Still, they do a nice job of maintaining the mystery, even as in part two things become more and more odd -- such as the day calendar that only reads 6th July. Part of the fun here is Milton Johns's portrayal of astronaut Guy Crayford, who's pitched at just the right level of control mixed with borderline hysteria. His scenes with the alien scientist Styggron are quite entertaining, particularly as Styggron has no interest in Crayford's feelings whatsoever. Plus, by including Crayford in the proceedings and adding his backstory (as told by Sarah) of a deep space astronaut who disappeared and was pronounced dead, they're able to keep the Earth pretense up. Having Benton and Harry Sullivan also walking around helps, even if they're not in these two episodes much and they're behaving strangely (because androids) when they are around.
But by the end of part two we've started to work things out, and thankfully the Doctor has as well: for whatever reason, this is just a very accurate facsimile of Earth. However, by this point the focus has shifted; Sarah has clearly been replaced by an android (with lots of clues for the viewers -- the Doctor mentions her scarf, but there's also the ginger pop stuff and the lack of a sprained ankle as sustained earlier in the episode), and in what's the most interesting cliffhanger of the story (and directed with some urgency, thankfully), "Sarah" is knocked back and her face falls off, revealing the android circuits inside...