The simple answer is that which X chromosome is inactivated varies in different cell lineages, so typically a female will have cells exhibiting either wild-type or mutant phenotypes. It was Mary Lyon's observation of mosaicism in heterozygous mouse coat colour that gave the phenomenon its name. So in the case of a recessive disease there will be a phenotype, but in many cases the 50% of cells expressing the normal gene will provide sufficient functional cells to get by. From the Wikipedia article about Mary Lyon:
Her research has allowed us to understand the genetic control mechanisms of chromosome X, which explains the absence of symptoms in numerous healthy women that are carriers of diseases associated with this chromosome.
Edit - response to comments:
Plug, I et al. (2006) Bleeding in carriers of hemophilia. Blood 108: 52-56
A wide range of factor VIII and IX levels is observed in heterozygous carriers of hemophilia as well as in noncarriers. In female carriers, extreme lyonization may lead to low clotting factor levels. We studied the effect of heterozygous hemophilia carriership on the occurrence of bleeding symptoms. A postal survey was performed among most of the women who were tested for carriership of hemophilia in the Netherlands before 2001. The questionnaire included items on personal characteristics, characteristics of hemophilia in the affected family members, and carrier testing and history of bleeding problems such as bleeding after tooth extraction, bleeding after tonsillectomy, and other operations. Information on clotting factor levels was obtained from the hospital charts. Logistic regression was used to assess the relation of carrier status and clotting factor levels with the occurrence of hemorrhagic events. In 2004, 766 questionnaires were sent, and 546 women responded (80%). Of these, 274 were carriers of hemophilia A or B. The median clotting factor level of carriers was 0.60 IU/mL (range, 0.05-2.19 IU/mL) compared with 1.02 IU/mL (range, 0.45-3.28 IU/mL) in noncarriers. Clotting factor levels from 0.60 to 0.05 IU/mL were increasingly associated with prolonged bleeding from small wounds and prolonged bleeding after tooth extraction, tonsillectomy, and operations. Carriers of hemophilia bleed more than other women, especially after medical interventions. Our findings suggest that not only clotting factor levels at the extreme of the distribution, resembling mild hemophilia, but also mildly reduced clotting factor levels between 0.41 and 0.60 IU/mL are associated with bleeding.
Bimler, D & Kirkland, J (2009) Colour-space distortion in women who are heterozygous for colour deficiency. Vision Research 49: 536-543
from the Introduction:
About 15% of women are heterozygous for some form of colour vision deficiency (CVD). That is, they possess a genetic abnormality on one of their two X chromosomes, affecting the photopigments (opsins) which subserve colour vision. The retina of a heterozygous woman is a mosaic in which some cone cells express the aberrant gene while others express the normal copy, depending on which X chromosome is active (inactivation of one X chromosome occurs randomly in retinal stem-cells at some stage of fetal development). The normal cells are sufficient to provide full trichromatic vision.