As with all NMR analysis problems like this, it is good to have a strategy to interpret data. Perhaps rather than looking at your spectrum and trying to rationalise your structure, look at your structure and predict what you might expect to see in your spectrum. You'll find it much easier to rationalise the appearance of your peaks, especially in the case of overlapping peaks as you have here.
So, in your molecule, what splitting would you expect?
You have 11 proton environments, so your integrals look fine. Your chloroform doublet is a bit of a worry though. Perhaps your sample needs to be mixed a little better? You've got 3 distinct spin systems that will give characteristic splittings:
- trans double bond. These two peaks will appear as distinct doublets, with couplings of around 12-17Hz. I can see one very clearly. The other, which we know to be upfield of the one at 7.77 because of the tenting is probably under the mess of stuff between 7.5-7.6. Being next to the carbonyl will have strong influence on the chemical shifts of these, and through a bit of electron-arrow pushing we can show that the proton closest to the carbonyl is shielded, and the other deshielded. Hence, the signal at 7.77 is likely to be your proton β to the carbonyl group (and closest to the para-substituted benzene ring)
- para-substituted benzene ring. Again a distinct splitting pattern; these will look like a pair of doublets (actually a second order pattern) with coupling about 7.5Hz. I can see one probably at 7.4. Its partner will also be under the mess between 7.5 and 7.6
- a mono-substituted benzene ring, which will have three sets of signal, with ratio 2:2:1. A carbonyl group is strongly electron withdrawing, deshielding the ortho protons, which is probably the signal up at about 8. The others.... under the mess between 7.5-7.6.
This is clearly a homework/lab problem, so this should be enough to keep you going until the next question.