Although both sounds are relatively close vowels, they differ in both tongue angle and length, so are unlikely to cause any confusion. The /ʊ/ vowel is relatively rare, ranking 17 out of the 20 vowel phonemes of English, which largely accounts for the relative shortness of this list.
The /i/ vowel appears in its common <ee> and <ea> spellings, along with <ie> in piece, <e> in besom and <iCe> in mystique. The /ʊ/ vowel is either <u> or <oo>, and is <oul> only in the modal verbs should, would and could.
Interesting pairs include:
besom bosom
heeded hooded
mystique mistook
The density figure is 1.9%. The number of semantic contrasts among the 77 pairs is 38, giving an unusually low semantic loading of 50%.
beach butch beak book beaks books beech butch besom bosom besoms bosoms chic shook creak crook creaked crooked creaking crooking creaks crooks creek crook creeks crooks feat foot feats foots feel full feeler fuller feelers fullers feet foot forefeet forefoot heed hood heeded hooded heeding hooding heeds hoods keyed could leak look leaked looked leaking looking leaks looks leek look leeks looks mystique mistook peace puss peach putsch peaches putsches peal pull pealed pulled pealing pulling peals pulls peat put peed pud peel pull peeled pulled peeling pulling peels pulls Pete put piece puss pieces pussies reek rook reeked rooked reeking rooking reeks rooks seat soot seated sooted seating sooting seats soots splayfeet splayfoot steed stood steep stoep steeps stoeps teak took tweed 'twould weal wool weals wools weed wood weeds woods weeded wooded weedy woody weedier woodier weediest woodiest weed would wheel wool wheels wools wreak rook wreaked rooked wreaking rooking wreaks rooks