I've edited your question somewhat; I hope I preserved its meaning.
Neuroticism relates to personal discomfort largely by definition, and probably to uncomfortable social interaction as well, though somewhat less by definition. Consider this hypothetical, mediated pathway:
Neuroticism $\rightarrow$ Anxiety $\rightarrow$ Social anxiety $\rightarrow$ Personal social discomfort $\rightarrow$ Others' discomfort
The first three of these paths are almost definitional; the last only assumes that people ordinarily feel more comfortable when interacting with others who are comfortable. Each step from neuroticism to others' discomfort changes the construct slightly, so the relationship attenuates across each step to whatever extent these mediators are all necessary, but I suspect the relationship is still reasonably strong from one end to the other. For a bit of empirical support (indirect – best I could find quickly), note that marriage satisfaction relates negatively to the neuroticism of one's partner (Fisher & McNulty, 2008), though this may be less true of women with neurotic husbands (Whiteford, 2010; for other moderators, see Larson, Blick, Jackson, & Holman, 2010).
The relationship between neuroticism and crime is somewhat more complex, largely because crime itself is diverse. Incarcerated populations are more neurotic (Dang & Sharma, 1995; Singh, Singh, Sinha, & Kumari, 1985; Eysenck & Eysenck, 1971; I also found support for this via negative emotionality in my own work as a research assistant in Robert Krueger's lab at the University of Minnesota in 2005), but neuroticism may not be the best trait predictor of delinquency (self-reported; Furnham & Thompson, 1991), antisocial behavior, or aggression – agreeableness seems to relate more strongly (negatively; Jones, Miller, & Lynam, 2011). Neuroticism relates to these, and to substance abuse and antisocial personality disorder, but not as strongly as to agreeableness or conscientiousness (both negative correlates; Ruiz, Pincus, & Schinka, 2008; see also Walters, 2014). Neuroticism doesn't predict criminal recidivism very well compared to demographic factors either (Gendreau, Little, & Goggin, 1996).
As @what implied in his response to your other question, "Would most people benefit from psychotherapy?" it seems safe enough to assume that anyone could benefit from psychotherapy, criminals included. Neuroticism is often undesirable from a personal standpoint, so neurotic individuals per se might be fairly motivated therapy clients, whereas antisocial personality disorder (ASPD) is more ego-syntonic. ASPD is notoriously difficult to treat, though this reputation may be debatable. Wikipedia:
ASPD is considered to be among the most difficult personality disorders to treat [(Gabbard & Gunderson, 2000)][verification needed]. Because of their very low or absent capacity for remorse, individuals with ASPD often lack sufficient motivation and fail to see the costs associated with antisocial acts...They may only simulate remorse rather than truly commit to change: they can be seductively charming and dishonest, and may manipulate staff and fellow patients during treatment [(Oldham, Skodol, & Bender, 2005)][verification needed]. Studies have shown that outpatient therapy is not likely to be successful, however the extent to which persons with ASPD are entirely unresponsive to treatment may have been exaggerated [(Salekin, 2002)].
Those with ASPD may stay in treatment only as required by an external source, such as a parole. Residential programs that provide a carefully controlled environment of structure and supervision along with peer confrontation have been recommended [(Gabbard & Gunderson, 2000)]. There has been some research on the treatment of ASPD that indicated positive results for therapeutic interventions [(Derefinko & Widiger, 2008)]. Schema Therapy is also being investigated as a treatment for ASPD [(Bernstein, Arntz, & Vos, 2007)]. A review by Charles M. Borduin features the strong influence of Multisystemic therapy (MST) that could potentially improve this imperative issue. However this treatment requires complete cooperation and participation of all family members [(Gatzke & Raine, 2000)]...
Therapists of individuals with ASPD may have considerable negative feelings toward clients with extensive histories of aggressive, exploitative, and abusive behaviors [(Gabbard & Gunderson, 2000)]. Rather than attempt to develop a sense of conscience in these individuals, therapeutic techniques should be focused on rational and utilitarian arguments against repeating past mistakes. These approaches would focus on the tangible, material value of prosocial behavior [(Beck, Freeman, & Davis, 2006); emphasis added].
An interesting interaction may occur between ASPD and neuroticism (via depression, a correlated emotional state) in predicting psychotherapeutic outcomes for substance abuse: patients with both ASPD and depression respond better than those with ASPD only (Gabbard, 2000). This further supports a mediated link between neuroticism and criminality:
Neuroticism $\rightarrow$ Substance abuse $\rightarrow$ Criminality
Neuroticism $\rightarrow$ Depression $\rightarrow$ Better outcomes for psychotherapy of substance abuse, given ASPD $\rightarrow$ Less recidivism? Worth testing at least!
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