[Rutherford]

The teacher doesn't know this, so I am doing it on my own.
I understand that the things you wrote are caused by the shielding effect, but I don't understand what are "semi" singlets and doublets. What H atom did you mean by "2 proton"?

[fledarmus]

Sorry, those "semi" things aren't anything formal to do with NMR spectroscopy - that is just my description of what I see when I look at the spectrum. Formally, if you have a 1,2,4 substituted benzene ring, then there would be protons on positions 3,5, and 6. The proton in the 3 position will be split by cross-ring coupling to both 5 and 6, but the couplings are so small that it usually just looks like a slightly broadened singlet, what I've called a "semi-singlet" and is the middle peak in the three peaks of the aromatic region you show in your first spectrum. The proton in the 6 position is coupled strongly by normal 3-bond coupling to the proton in the 5 position (which is ortho to it), which gives a doublet, and very weakly by cross-ring coupling to the 3 proton (para), so it still looks mostly like a doublet - what I've called a "semi-doublet" and which is the right peak set on your spectrum. The proton in the 5 position is coupled strongly to the proton in the 6 position (ortho_ to give a doubly, and weakly to the proton in the 3 position (meta), but somewhat more strongly to 3 than 6 is. That makes it look sort of like a doublet of doublets, usually with some fine structure, and shows the shape on the left peak set on your spectrum. If you expand the aromatic region in a high-field NMR you can see much more detail, but I thought these rough descriptions would suffice for the problem at hand.

I got the term "2 proton" from your nomenclature. If you have 3,4-dichloroacetophenone, then you will have protons attached to your benzene ring at positions 2, 5, and 6. Position 1 has your ketone, and positions 3 and 4 have your chlorines. The 2 proton would be the isolated one between the ketone and the chlorines.

[Rutherford]

Why does the doublet of doublets appear, and why did you assign for 3,4-dichloroacetophenone 6 to be dd, and for 2,4-dichloroacetophenone 5 to be dd?

[orgopete]

…Using this table, you can calculate (for 2,4-dichloroacetophenone) the 6 proton to be about 7.82, the 3 proton to be about 7.50, and the 5 proton to be 7.31.

Thanks for doing the calculations. I refer to the coupling from the benzene coupling constants, J_1,2 ~6-7Hz, J_1,3 ~1-2Hz, and J_1,4 ~0Hz as lg-large and sm-small. Let me summarize,
SDBS spectrum:
H3 7.43 (sm),
H5 7.32 (lg), and
H6 7.53 (lg,sm).

Calculated
H3 7.42 (sm),
H5 7.31 (lg), and
H6 7.82 (lg,sm).

Although the calculations can be somewhat ambiguous, especially as they do not accurately predict the chemical shift. I would say you would have to compare the pattern of the chemical shifts. (I don't remember what I used as an example, but I tried to make the assignments to be based upon the coupling constants rather than requires the substituent calculation. It would have been too much work to find examples and to also calculate what the chemical shifts ought to be. Use a nitro group, its ortho chemical shift is large and if there isn't a para, they are almost unambiguous.) 

For the 3',4'- isomer, SDBS
H2 8.01 (sm),
H5 7.54 (lg), and
H6 7.76 (lg,sm).

Calcd
H2 7.87 (sm)
H5 7.37 (lg)
H6 7.76 (lg,sm)