I think that separation of observation and inference is part of the question. Rephrasing the question says that putting words on an observation (at least to describe it) builds upon something that is in your mind and prior to the observation.

Many important philosophers have tryed to dig into the mirage of the scientific objectivity, before and after Popper. I have tried to come to you with few words about some of my favorites. Also I'm french and scientific and it is structured into 3 parts.

1 - Popper is using his scientific mind to dig into science's language and that's a problem.

I find the words of Biran very appealing about that

Quand nous creusons dans la vérité pour la pénétrer, elle creuse aussi en nous pour prendre possession de nos âmes.

and Heraclite's words are full of similar ideas, e.g.

(Fgt1, sextus Empiricus, Contre les mathématiciens) Though this discourse if true evermore, yet men are as unable to understand it when they hear it for the first time as before they have heard it at all. For, although, all things happen in accordance with the account I give men seem as if they have no experience of them, when they make trial of words and works such as I set forth, dividing each thing according to its nature and explaining how it truly is. But other men know not what they are doing when you wake them up, just as they forget, what they do when asleep. (Fgt 2) wisdom is common, yet the many live as if they had a wisdom of their own (Fgt 7) If all things were turned to smoke, the nostrils would distinguish them (Fgt 17) The many have not as many thoughts as the things they meet with; nor, if they do remark them, do they understand them, though they believe they do.

2- The separation of observation/experiment/theory is not that obvious

It is neither a survey nor a response to Popper's theory but Différences et Répétitions from Gilles Deleuze is turning around this interface that we try to build with the real world. Hard to quote some particular sentence, this book is long to read...

A very interesting science that has to face the problem is linguistic or Language theory and I would advise you to get into papers from Noam Chomsky (he wrote a few very philosophical paper, I have to find them again). There observation, the description of observation and the theory behind observations are not easy to distinguish :).

@RexKerr mentioned a case with a proportion of someone doing something. In this case it appears that observation can be distinguished from the inference that can be done from it. I could suggest, in line with difference et répetition that repeating the same experiment a given number of time is part of a mental process but that would not be my principal grievance about this argument. Wittgenstein, in On Certainty showed the lack of thickness of things that can be said to be "certain" (like observations...).

3- The scientific endless effort toward objectivity is a lot of burden for a little value

EDIT according to @RexKerr comments: This formulation is a bit strong, maybe one could say that objectivity, while being necessary at some point, is not a sufficient condition for a good philosophy and that too much emphasys on objectivity might lead to a loss of something more fundamental. End of EDIT

With the tractacus Wittgenstein claims that there are things that can be shown and things that can be said. Things that can be said are undoubted things that could be connected with the certainties (on certainty however was written much latter). In tractacus, the point is not that the set of certainties has no thicknes but that it has no real "value" (for it is only rephrasing of something obvious) while things that can be shown are projecting a deeper aspect of human being. I like that Wittgenstein being definitively mystical. So was Heraclite:

(Fgt 9) Asses would rather have straw than gold (Fgt 22) Those who seek for gold dig up much earth and find a little (Fgt 18) if you do not expect the unexpected, you will not find it; for it is hard to be sought out and difficult. (Fgt 101) Eyes are more exact witnesses than ears. (Fgt 107) Eyes and ears are bad witnesses to men, if they have souls that understand not their language.

Nietsche says something like "mathematician prefer to spend their life building a bridge to cross the river while I'm more jupping from rock to rock" (I don't remember the exact sentence, even in French, but it's in Philosophy in the Tragic Age of the Greeks), and I think he was inspired by Heraclite there.

Finally the book of Foucault "les mots et les choses" is really illustrating how the way to approach things "scientifically" (ok that's not physic and math but language, natural science and economy :) ) has changed during the years and how this was connected to some deeper aspect of human been and his cultural evolution (focusing there on the European culture).

Related questions: I would say I had something like that in mind when I wrote the questions When and why do we say that two things are the same? and When can we call an explanation "rational"?

and answers there might help you.