The International Olympic Committee is still deliberating on whether 250 Russian athletes can participate.
Brazil, facing political and economic crises as well, has suffered repeated stumbles in the run-up to hosting the world's biggest sporting event.
Hundreds of peaceful protesters have marched on Rio's Copacabana Beach, calling for suspended Brazilian president Dilma Rousseff to be permanently removed from office.
But her supporters are threatening protests of their own on Friday, the day of the opening ceremony of the Olympic Games.
The International Olympic Committee has enough trouble after deciding not to ban all Russian athletes following revelations of a wide, state-backed doping program across many sports.
The IOC had left the decision on whether individual athletes could participate up to the individual sport bodies.
But it now says the committee will have the final say and has announced a three-person panel to decide the fate of athletes whose federations had cleared to compete.
IOC president Thomas Bach is defending that decision.
"I don't think that this, in the end, will be damaging, because people will realise that we have to take this decision now. And imagine the situation if we would not have taken a decision. What the limbo would be then? I trust the people that they realise the difficulties we are in."
But there is concern the decision leaves little time for replacements -- and, potentially, a whole team -- to be flown in.
The Russsian Olympic Committee's Evgeny Granov says Russian athletes already in Rio remain in limbo, uncertain whether they will be allowed to compete.
"Of course, it's not easy, because the most difficult thing is emotional pressure for the athletes, because they don't know if they'll be in the Olympic Games or not. For those who are not dopers, it's not fair."
And as Brazilian organisers rush to prepare venues ahead of Friday, health officials continue to downplay other concerns such as the threat of the Zika virus and water pollution.
Some tourists do not appear very concerned, though.
"If you think about it rationally and look at the numbers, one can get all sorts of illnesses when you're travelling. It was on our minds, but we are not especially concerned about it now. We considered it, for sure, but it didn't stop us from coming to Brazil."
"Actually, I came from Australia, so, in Australia, they told us some ways that you can protect yourself against Zika, to use some mosquito spray and some medicine. So, yeah, should be fine. I'm using it, and I don't worry about it."
And to add to Rio's woes, high waves, up to three metres high, have damaged infrastructure at the Olympic sailing venue.
They have also pounded the Olympic television studios along Copacabana Beach.
Engineer Sergio Gontgio suggests it may not have been the best location to house broadcasting facilities.
"Look at it here. They're going to see very well that it's a place where this always happens. It's the worst place on the beach. It always happens here, this type of crashing wave. They picked the worst place that they could."
