Good advice on decoupling 5V, but not good advice about adding 0.1 uF across the 47 uF. In some instances, for example using a large electrolytic capacitor with high ESR/ESL this could help with high frequency noise, however tantalum devices are likely as good as the ceramic in this case, so this will not do anything useful and will drive you crazy trying to solder it on. Worse, in some cases, you could introduce instability with a second pole in the filter, so this approach should be used with caution. And adding caps to the data lines will reduce the range and degrade the signal - very bad idea. Also twisted pair will be more harmful than helpful in this instance, since the signal is unbalanced.
Honestly, the problem is most likely the poor 3V supply - fix that before investing any time in other approaches.
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